Let's assume that Johan practiced on x weekdays.
On Saturday, he practiced for 45 minutes.
On the rest of the weekdays, he practiced for 25 minutes each.
So, he practiced for (x + 1) days in total.
On Saturday, he practiced for 45 minutes, and on the rest of the weekdays, he practiced for 25 minutes each.
Therefore, the total time he practiced last week is 45 + 25x.
According to the problem, the total time he practiced last week is 120 minutes.
So, we can write the equation as:
45 + 25x = 120
14. Johan practices the drums for 45 minutes on Saturday and 25 minutes on most weekdays. Last week he practiced 120 minutes. How many weekdays did he practice? Write an equation in the form of px + q = r to represent this problem.(3 points)
11 answers
15. Jack won 65 lollipops playing basketball at the county fair. At school he gave four to every student in his math class. He only has 1 remaining. How many students are in his class?(1 point)
Let's assume there are x students in Jack's math class.
Jack gave four lollipops to each student, so the total number of lollipops given out is 4x.
Jack won 65 lollipops and has 1 remaining, so the total number of lollipops is 65 + 1 = 66.
Therefore, we can write the equation as:
4x + 1 = 66
Jack gave four lollipops to each student, so the total number of lollipops given out is 4x.
Jack won 65 lollipops and has 1 remaining, so the total number of lollipops is 65 + 1 = 66.
Therefore, we can write the equation as:
4x + 1 = 66
wrong the answer is 16
Apologies for the mistake. You are correct. If Jack gave four lollipops to every student in his math class, and he has one remaining after giving them out, then we can write the equation as:
4x + 1 = 65
Simplifying this equation:
4x = 65 - 1
4x = 64
x = 64/4
x = 16
Therefore, there are 16 students in Jack's math class.
4x + 1 = 65
Simplifying this equation:
4x = 65 - 1
4x = 64
x = 64/4
x = 16
Therefore, there are 16 students in Jack's math class.
16. Angela earns a weekly allowance at the start of each week. She started the week with just her weekly allowance. Then, she spent half of her weekly allowance at the movies. To earn more money, her parents let her clean the windows in the house for $5. What is her weekly allowance if she ended the week with $8? Solve using arithmetic or algebra, and explain your steps.(3 points)
Let's assume Angela's weekly allowance is x dollars.
Angela spent half of her weekly allowance at the movies, which is (1/2)x dollars.
Angela's parents paid her $5 for cleaning the windows.
So, at the end of the week, Angela has x - (1/2)x + $5 = $8.
Combining like terms, we have (1/2)x + $5 = $8.
Subtracting $5 from both sides of the equation, we get (1/2)x = $3.
To solve for x, we multiply both sides of the equation by 2/1 (or just 2):
(2/1) * (1/2)x = (2/1) * $3.
This simplifies to x = $6.
Therefore, Angela's weekly allowance is $6.
Angela spent half of her weekly allowance at the movies, which is (1/2)x dollars.
Angela's parents paid her $5 for cleaning the windows.
So, at the end of the week, Angela has x - (1/2)x + $5 = $8.
Combining like terms, we have (1/2)x + $5 = $8.
Subtracting $5 from both sides of the equation, we get (1/2)x = $3.
To solve for x, we multiply both sides of the equation by 2/1 (or just 2):
(2/1) * (1/2)x = (2/1) * $3.
This simplifies to x = $6.
Therefore, Angela's weekly allowance is $6.
wrong her total money at the end of the week is 8
Apologies for the confusion. Let's solve the problem again with the correct information.
Let's assume Angela's weekly allowance is x dollars.
Angela spent half of her weekly allowance at the movies, which is (1/2)x dollars.
She also received $5 for cleaning the windows in the house.
At the end of the week, Angela has her initial allowance (x) minus the amount spent at the movies ((1/2)x) plus the amount earned from cleaning the windows ($5), and this total is $8.
So, we can write the equation as:
x - (1/2)x + $5 = $8
To simplify the equation, we first combine like terms:
(1/2)x + $5 = $8
Next, we subtract $5 from both sides of the equation:
(1/2)x = $8 - $5
(1/2)x = $3
To solve for x, we multiply both sides of the equation by 2/1 (or just 2):
(2/1) * (1/2)x = (2/1) * $3
This simplifies to:
x = $6
Therefore, Angela's weekly allowance is $6.
Let's assume Angela's weekly allowance is x dollars.
Angela spent half of her weekly allowance at the movies, which is (1/2)x dollars.
She also received $5 for cleaning the windows in the house.
At the end of the week, Angela has her initial allowance (x) minus the amount spent at the movies ((1/2)x) plus the amount earned from cleaning the windows ($5), and this total is $8.
So, we can write the equation as:
x - (1/2)x + $5 = $8
To simplify the equation, we first combine like terms:
(1/2)x + $5 = $8
Next, we subtract $5 from both sides of the equation:
(1/2)x = $8 - $5
(1/2)x = $3
To solve for x, we multiply both sides of the equation by 2/1 (or just 2):
(2/1) * (1/2)x = (2/1) * $3
This simplifies to:
x = $6
Therefore, Angela's weekly allowance is $6.
John is cooking cupcakes. The recipe calls for 3 3/10 cups of flour. He accidentally put in 3 5/8 cups of flour. How many extra cups did he put in?(1 point) Responses
To find the number of extra cups of flour John put in, we need to subtract the correct amount of flour needed from the amount he actually put in.
The correct amount of flour needed is 3 3/10 cups.
The amount John actually put in is 3 5/8 cups.
To subtract these two quantities, we need to find a common denominator.
The denominator of 10 and the denominator of 8 have a common multiple of 40.
So, let's convert both mixed numbers to fractions with a denominator of 40.
3 3/10 is equal to (3 * 10 + 3)/10 = 33/10.
3 5/8 is equal to (3 * 8 + 5)/8 = 29/8.
Now we can subtract:
29/8 - 33/10.
To subtract fractions, we need to have a common denominator.
The common denominator is 40.
So, let's rewrite the fractions:
(29 * 5)/(8 * 5) - (33 * 4)/(10 * 4).
This becomes:
145/40 - 132/40.
Now we can subtract:
145/40 - 132/40 = (145 - 132)/40 = 13/40.
Therefore, John put in an extra 13/40 cups of flour.
The correct amount of flour needed is 3 3/10 cups.
The amount John actually put in is 3 5/8 cups.
To subtract these two quantities, we need to find a common denominator.
The denominator of 10 and the denominator of 8 have a common multiple of 40.
So, let's convert both mixed numbers to fractions with a denominator of 40.
3 3/10 is equal to (3 * 10 + 3)/10 = 33/10.
3 5/8 is equal to (3 * 8 + 5)/8 = 29/8.
Now we can subtract:
29/8 - 33/10.
To subtract fractions, we need to have a common denominator.
The common denominator is 40.
So, let's rewrite the fractions:
(29 * 5)/(8 * 5) - (33 * 4)/(10 * 4).
This becomes:
145/40 - 132/40.
Now we can subtract:
145/40 - 132/40 = (145 - 132)/40 = 13/40.
Therefore, John put in an extra 13/40 cups of flour.
1 answer