To solve for w, let's first isolate the variable on one side of the equation by moving the constant to the other side:
-23 = -3 + 5w
Adding 3 to both sides:
-23 + 3 = -3 + 3 + 5w
-20 = 5w
Now, divide both sides of the equation by 5:
-20/5 = 5w/5
-4 = w
So, the solution to the equation is w = -4.
-23=-3+5w
solve for w
simplify answer as much as possible
37 answers
-5=u/2+5
solve for u
simplify answer as much as possible
solve for u
simplify answer as much as possible
To solve for u, let's first isolate the variable on one side of the equation by moving the constant to the other side:
-5 = u/2 + 5
Subtracting 5 from both sides:
-5 - 5 = u/2 + 5 - 5
-10 = u/2
Now, multiply both sides of the equation by 2:
-10 * 2 = (u/2) * 2
-20 = u
So, the solution to the equation is u = -20.
-5 = u/2 + 5
Subtracting 5 from both sides:
-5 - 5 = u/2 + 5 - 5
-10 = u/2
Now, multiply both sides of the equation by 2:
-10 * 2 = (u/2) * 2
-20 = u
So, the solution to the equation is u = -20.
Integers that follow one after the other without "gaps" are called integers.
Part 2 of 6
(b) The integers , , , and are examples of consecutive integers.
Part 3 of 6
(c) The integers , , , and are examples of consecutive integers.
Part 4 of 6
(d) Two consecutive integers differ by
.
Part 5 of 6
(e) Two consecutive odd integers differ by
.
Part 6 of 6
(f) Two consecutive even integers differ by
.
Part 2 of 6
(b) The integers , , , and are examples of consecutive integers.
Part 3 of 6
(c) The integers , , , and are examples of consecutive integers.
Part 4 of 6
(d) Two consecutive integers differ by
.
Part 5 of 6
(e) Two consecutive odd integers differ by
.
Part 6 of 6
(f) Two consecutive even integers differ by
.
Part 2 of 6:
The integers -3, -2, -1, and 0 are examples of consecutive integers.
Part 3 of 6:
The integers 5, 6, 7, and 8 are examples of consecutive integers.
Part 4 of 6:
Two consecutive integers differ by 1.
Part 5 of 6:
Two consecutive odd integers differ by 2.
Part 6 of 6:
Two consecutive even integers differ by 2.
The integers -3, -2, -1, and 0 are examples of consecutive integers.
Part 3 of 6:
The integers 5, 6, 7, and 8 are examples of consecutive integers.
Part 4 of 6:
Two consecutive integers differ by 1.
Part 5 of 6:
Two consecutive odd integers differ by 2.
Part 6 of 6:
Two consecutive even integers differ by 2.
Write an expression representing the unknown quantity.
At a recent motorcycle rally, the number of men exceeded the number of women by 294. If x represents the number of women, write an expression for the number of men.
The number of men can be represented by the expression
At a recent motorcycle rally, the number of men exceeded the number of women by 294. If x represents the number of women, write an expression for the number of men.
The number of men can be represented by the expression
x + 294.
Write an expression representing the unknown quantity.
Sidney made $26 more than seven times Casey's weekly salary. If x represents Casey's weekly salary, write an expression for Sidney's weekly salary.
Sidney's weekly salary can be represented by the expression
.
Sidney made $26 more than seven times Casey's weekly salary. If x represents Casey's weekly salary, write an expression for Sidney's weekly salary.
Sidney's weekly salary can be represented by the expression
.
Sidney's weekly salary can be represented by the expression 7x + 26.
Write an expression representing the unknown quantity.
David scored 27 points less than seven times the number of points Rich scored in a video game. If x represents the number of points scored by Rich, write an expression representing the number of points scored by David.
The number of points scored by David can be represented by the expression
David scored 27 points less than seven times the number of points Rich scored in a video game. If x represents the number of points scored by Rich, write an expression representing the number of points scored by David.
The number of points scored by David can be represented by the expression
7x - 27.
Seventeen less than a number is -19. Find the number. Round your answer to the nearest integer, if necessary
To find the number, we can set up the equation:
x - 17 = -19
Adding 17 to both sides of the equation:
x - 17 + 17 = -19 + 17
x = -2
Therefore, the number is -2.
x - 17 = -19
Adding 17 to both sides of the equation:
x - 17 + 17 = -19 + 17
x = -2
Therefore, the number is -2.
Four times the sum of a number and four is eight. Find the number. Round your answer to the nearest integer, if necessary
To find the number, we can set up the equation:
4(x + 4) = 8
Expanding the equation:
4x + 16 = 8
Subtracting 16 from both sides of the equation:
4x + 16 - 16 = 8 - 16
4x = -8
Dividing both sides of the equation by 4:
x = -2
Therefore, the number is -2.
4(x + 4) = 8
Expanding the equation:
4x + 16 = 8
Subtracting 16 from both sides of the equation:
4x + 16 - 16 = 8 - 16
4x = -8
Dividing both sides of the equation by 4:
x = -2
Therefore, the number is -2.
A number added to four is the same as three times the number. Find the number. Round your answer to the nearest integer, if necessary.
To find the number, we can set up the equation:
x + 4 = 3x
Subtracting x from both sides of the equation:
x + 4 - x = 3x - x
4 = 2x
Dividing both sides of the equation by 2:
2 = x
Therefore, the number is 2.
x + 4 = 3x
Subtracting x from both sides of the equation:
x + 4 - x = 3x - x
4 = 2x
Dividing both sides of the equation by 2:
2 = x
Therefore, the number is 2.
The sum of three times a number and seven is equal to the difference of the number and thirteen. Find the number. Round your answer to the nearest integer, if necessary.
To find the number, let's set up the equation:
3x + 7 = x - 13
Subtracting x from both sides of the equation:
3x + 7 - x = x - x - 13
2x + 7 = -13
Subtracting 7 from both sides of the equation:
2x + 7 - 7 = -13 - 7
2x = -20
Dividing both sides of the equation by 2:
x = -10
Therefore, the number is -10.
3x + 7 = x - 13
Subtracting x from both sides of the equation:
3x + 7 - x = x - x - 13
2x + 7 = -13
Subtracting 7 from both sides of the equation:
2x + 7 - 7 = -13 - 7
2x = -20
Dividing both sides of the equation by 2:
x = -10
Therefore, the number is -10.
The sum of two consecutive odd integers is 40. Find the integers.
Let's denote the first odd integer as x. Since it is consecutive to the first odd integer, the second odd integer will be x + 2.
The sum of the two consecutive odd integers is given as 40, so we can form the equation:
x + (x + 2) = 40
Simplifying the equation:
2x + 2 = 40
Subtracting 2 from both sides:
2x = 38
Dividing both sides of the equation by 2:
x = 19
So, the first odd integer is 19, and the second odd integer is 19 + 2 = 21.
Therefore, the two consecutive odd integers that sum up to 40 are 19 and 21.
The sum of the two consecutive odd integers is given as 40, so we can form the equation:
x + (x + 2) = 40
Simplifying the equation:
2x + 2 = 40
Subtracting 2 from both sides:
2x = 38
Dividing both sides of the equation by 2:
x = 19
So, the first odd integer is 19, and the second odd integer is 19 + 2 = 21.
Therefore, the two consecutive odd integers that sum up to 40 are 19 and 21.
For a recent year, the number of men in the U.S. Senate totaled 4 more than 3 times the number of women. Find the number of men and the number of women in the Senate given that the Senate has 100 members.
Let's denote the number of women in the Senate as x. Since the total number of members in the Senate is 100, the number of men in the Senate would be 100 - x.
According to the given information, the number of men in the Senate is 4 more than 3 times the number of women. Therefore, we can form the equation:
100 - x = 3x + 4
Simplifying the equation:
100 = 4x + x + 4
Combining like terms:
100 = 5x + 4
Subtracting 4 from both sides:
96 = 5x
Dividing both sides by 5:
x = 19.2
However, since we are dealing with the number of people, x must be a whole number. Therefore, we round 19.2 down to the nearest whole number, which is 19.
So, there are 19 women in the Senate. Substituting this value back into our equation to find the number of men:
100 - x = 100 - 19 = 81
Therefore, there are 81 men in the Senate.
To summarize:
Number of women in the Senate: 19
Number of men in the Senate: 81
According to the given information, the number of men in the Senate is 4 more than 3 times the number of women. Therefore, we can form the equation:
100 - x = 3x + 4
Simplifying the equation:
100 = 4x + x + 4
Combining like terms:
100 = 5x + 4
Subtracting 4 from both sides:
96 = 5x
Dividing both sides by 5:
x = 19.2
However, since we are dealing with the number of people, x must be a whole number. Therefore, we round 19.2 down to the nearest whole number, which is 19.
So, there are 19 women in the Senate. Substituting this value back into our equation to find the number of men:
100 - x = 100 - 19 = 81
Therefore, there are 81 men in the Senate.
To summarize:
Number of women in the Senate: 19
Number of men in the Senate: 81
there were actually 24 women and 76 men
Apologies for the incorrect response earlier. Let's recalculate based on the corrected information.
Let's denote the number of women in the Senate as x. Since the total number of members in the Senate is 100, the number of men in the Senate would be 100 - x.
According to the given information, the number of men in the Senate is 4 more than 3 times the number of women. Therefore, we can form the equation:
100 - x = 3x + 4
Simplifying the equation:
100 = 4x + x + 4
Combining like terms:
100 = 5x + 4
Subtracting 4 from both sides:
96 = 5x
Dividing both sides by 5:
x = 19.2
However, since we are dealing with the number of people, x must be a whole number. Therefore, we round 19.2 up to the nearest whole number, which is 20.
So, there are 20 women in the Senate. Substituting this value back into our equation to find the number of men:
100 - x = 100 - 20 = 80
Therefore, there are 80 men in the Senate.
To summarize:
Number of women in the Senate: 20
Number of men in the Senate: 80
Let's denote the number of women in the Senate as x. Since the total number of members in the Senate is 100, the number of men in the Senate would be 100 - x.
According to the given information, the number of men in the Senate is 4 more than 3 times the number of women. Therefore, we can form the equation:
100 - x = 3x + 4
Simplifying the equation:
100 = 4x + x + 4
Combining like terms:
100 = 5x + 4
Subtracting 4 from both sides:
96 = 5x
Dividing both sides by 5:
x = 19.2
However, since we are dealing with the number of people, x must be a whole number. Therefore, we round 19.2 up to the nearest whole number, which is 20.
So, there are 20 women in the Senate. Substituting this value back into our equation to find the number of men:
100 - x = 100 - 20 = 80
Therefore, there are 80 men in the Senate.
To summarize:
Number of women in the Senate: 20
Number of men in the Senate: 80
A group of hikers walked from Hawk Mt. Shelter to Blood Mt. Shelter along the Appalachian Trail, a total distance of 13.1 mi. It took 2days for the walk. The second day the hikers walked 2.8 mi less than they did on the first day. How far did they walk each day?
Let's denote the distance walked on the first day as x. Since the hikers walked 2.8 mi less on the second day, the distance walked on the second day would be x - 2.8.
According to the given information, the total distance walked is 13.1 mi and it took 2 days. Therefore, we can form the equation:
x + (x - 2.8) = 13.1
Simplifying the equation:
2x - 2.8 = 13.1
Adding 2.8 to both sides:
2x - 2.8 + 2.8 = 13.1 + 2.8
2x = 15.9
Dividing both sides of the equation by 2:
x = 7.95
However, since we are dealing with distance, x must be a whole number. Therefore, we round 7.95 to the nearest whole number, which is 8.
So, the hikers walked 8 miles on the first day. Substituting this value back into our equation to find the distance on the second day:
x - 2.8 = 8 - 2.8 = 5.2
Therefore, the hikers walked 8 miles on the first day and 5.2 miles on the second day.
To summarize:
Distance walked on the first day: 8 miles
Distance walked on the second day: 5.2 miles
According to the given information, the total distance walked is 13.1 mi and it took 2 days. Therefore, we can form the equation:
x + (x - 2.8) = 13.1
Simplifying the equation:
2x - 2.8 = 13.1
Adding 2.8 to both sides:
2x - 2.8 + 2.8 = 13.1 + 2.8
2x = 15.9
Dividing both sides of the equation by 2:
x = 7.95
However, since we are dealing with distance, x must be a whole number. Therefore, we round 7.95 to the nearest whole number, which is 8.
So, the hikers walked 8 miles on the first day. Substituting this value back into our equation to find the distance on the second day:
x - 2.8 = 8 - 2.8 = 5.2
Therefore, the hikers walked 8 miles on the first day and 5.2 miles on the second day.
To summarize:
Distance walked on the first day: 8 miles
Distance walked on the second day: 5.2 miles
The sum of the page numbers on two facing pages in a book is 937. What are the page numbers?
Let's denote the page number on one of the facing pages as x. Since the sum of the page numbers on the two facing pages is 937, the page number on the other facing page would be x + 1 (since consecutive page numbers in a book are always one apart).
According to the given information, the sum of the page numbers is 937. Therefore, we can form the equation:
x + (x + 1) = 937
Simplifying the equation:
2x + 1 = 937
Subtracting 1 from both sides:
2x + 1 - 1 = 937 - 1
2x = 936
Dividing both sides of the equation by 2:
x = 468
So, the page number on one of the facing pages is 468. Substituting this value back into our equation to find the page number on the other facing page:
x + 1 = 468 + 1 = 469
Therefore, the page numbers on the two facing pages are 468 and 469.
To summarize:
Page number on the first facing page: 468
Page number on the second facing page: 469
According to the given information, the sum of the page numbers is 937. Therefore, we can form the equation:
x + (x + 1) = 937
Simplifying the equation:
2x + 1 = 937
Subtracting 1 from both sides:
2x + 1 - 1 = 937 - 1
2x = 936
Dividing both sides of the equation by 2:
x = 468
So, the page number on one of the facing pages is 468. Substituting this value back into our equation to find the page number on the other facing page:
x + 1 = 468 + 1 = 469
Therefore, the page numbers on the two facing pages are 468 and 469.
To summarize:
Page number on the first facing page: 468
Page number on the second facing page: 469
$140 is to be divided among three restaurant servers. Angie made $20 more than Marie. Gwen, who went home sick, made $27 less than Marie. How much money should each server get?
Let's denote the amount of money Marie made as x.
According to the given information:
1. Angie made $20 more than Marie, so Angie made x + $20.
2. Gwen made $27 less than Marie, so Gwen made x - $27.
The sum of the amounts that Angie, Marie, and Gwen made should add up to $140.
Therefore, we can form the equation:
(x + $20) + x + (x - $27) = $140
Combining like terms:
3x - $7 = $140
Adding $7 to both sides:
3x - $7 + $7 = $140 + $7
3x = $147
Dividing both sides of the equation by 3:
x = $49
So, Marie made $49. Substituting this value back into our information to find how much Angie and Gwen made:
Angie made $20 more than Marie:
Angie made $49 + $20 = $69
Gwen made $27 less than Marie:
Gwen made $49 - $27 = $22
Therefore, the distribution of the $140 among the three servers would be as follows:
Angie: $69
Marie: $49
Gwen: $22
According to the given information:
1. Angie made $20 more than Marie, so Angie made x + $20.
2. Gwen made $27 less than Marie, so Gwen made x - $27.
The sum of the amounts that Angie, Marie, and Gwen made should add up to $140.
Therefore, we can form the equation:
(x + $20) + x + (x - $27) = $140
Combining like terms:
3x - $7 = $140
Adding $7 to both sides:
3x - $7 + $7 = $140 + $7
3x = $147
Dividing both sides of the equation by 3:
x = $49
So, Marie made $49. Substituting this value back into our information to find how much Angie and Gwen made:
Angie made $20 more than Marie:
Angie made $49 + $20 = $69
Gwen made $27 less than Marie:
Gwen made $49 - $27 = $22
Therefore, the distribution of the $140 among the three servers would be as follows:
Angie: $69
Marie: $49
Gwen: $22
The average depth of one sea is four times the depth of a second sea. The difference between the average depths is 1308 m. What is the average depth of the first and the second sea? Round your answers to the nearest meter, if necessary.
Let's denote the depth of the second sea as x.
According to the given information, the average depth of the first sea is four times the depth of the second sea. Therefore, the average depth of the first sea would be 4x.
The difference between the average depths is given as 1308 m. So, we can form the equation:
4x - x = 1308
Simplifying the equation:
3x = 1308
Dividing both sides of the equation by 3:
x = 436
Therefore, the depth of the second sea is 436 meters.
To find the average depth of the first sea, we substitute this value back into our equation:
4x = 4 * 436 = 1744
Therefore, the average depth of the first sea is 1744 meters.
To summarize:
Depth of the second sea: 436 meters
Depth of the first sea: 1744 meters
According to the given information, the average depth of the first sea is four times the depth of the second sea. Therefore, the average depth of the first sea would be 4x.
The difference between the average depths is given as 1308 m. So, we can form the equation:
4x - x = 1308
Simplifying the equation:
3x = 1308
Dividing both sides of the equation by 3:
x = 436
Therefore, the depth of the second sea is 436 meters.
To find the average depth of the first sea, we substitute this value back into our equation:
4x = 4 * 436 = 1744
Therefore, the average depth of the first sea is 1744 meters.
To summarize:
Depth of the second sea: 436 meters
Depth of the first sea: 1744 meters
A board is 75cm in length and must be cut so that one piece is 17cm longer than the other piece. Find the length of each piece. Round your answers to the nearest centimeter, if necessary.
Let's denote the length of one piece of the board as x cm.
According to the given information, the other piece of the board must be 17 cm longer than the first piece. Therefore, the length of the other piece would be x + 17 cm.
The total length of the board is 75 cm, so we can set up the equation:
x + (x + 17) = 75
Simplifying the equation:
2x + 17 = 75
Subtracting 17 from both sides:
2x = 58
Dividing both sides of the equation by 2:
x = 29
Therefore, one piece of the board is 29 cm long.
Substituting this value back into our equation to find the length of the other piece:
x + 17 = 29 + 17 = 46
Therefore, the other piece of the board is 46 cm long.
To summarize:
Length of one piece of the board: 29 cm
Length of the other piece of the board: 46 cm
According to the given information, the other piece of the board must be 17 cm longer than the first piece. Therefore, the length of the other piece would be x + 17 cm.
The total length of the board is 75 cm, so we can set up the equation:
x + (x + 17) = 75
Simplifying the equation:
2x + 17 = 75
Subtracting 17 from both sides:
2x = 58
Dividing both sides of the equation by 2:
x = 29
Therefore, one piece of the board is 29 cm long.
Substituting this value back into our equation to find the length of the other piece:
x + 17 = 29 + 17 = 46
Therefore, the other piece of the board is 46 cm long.
To summarize:
Length of one piece of the board: 29 cm
Length of the other piece of the board: 46 cm
The perimeter of a pentagon (a five-sided polygon) is 65 in. The five sides are represented by consecutive integers. Find the lengths of the sides.
Let's represent the lengths of the five consecutive sides of the pentagon as x, x+1, x+2, x+3, and x+4.
The perimeter of a pentagon is the sum of the lengths of its sides.
So, we can form the equation:
x + (x+1) + (x+2) + (x+3) + (x+4) = 65
Simplifying the equation:
5x + 10 = 65
Subtracting 10 from both sides:
5x = 55
Dividing both sides of the equation by 5:
x = 11
Therefore, the lengths of the five sides of the pentagon are:
1st side: x = 11
2nd side: x+1 = 12
3rd side: x+2 = 13
4th side: x+3 = 14
5th side: x+4 = 15
So, the lengths of the sides of the pentagon are 11, 12, 13, 14, and 15.
The perimeter of a pentagon is the sum of the lengths of its sides.
So, we can form the equation:
x + (x+1) + (x+2) + (x+3) + (x+4) = 65
Simplifying the equation:
5x + 10 = 65
Subtracting 10 from both sides:
5x = 55
Dividing both sides of the equation by 5:
x = 11
Therefore, the lengths of the five sides of the pentagon are:
1st side: x = 11
2nd side: x+1 = 12
3rd side: x+2 = 13
4th side: x+3 = 14
5th side: x+4 = 15
So, the lengths of the sides of the pentagon are 11, 12, 13, 14, and 15.
0 answers