1. j + c = 54
2. j = 2c + 3
To solve, we can use substitution:
Substitute the second equation into the first:
(2c + 3) + c = 54
Simplify:
3c + 3 = 54
Subtract 3 from both sides:
3c = 51
Divide both sides by 3:
c = 17
Now we can use this value to find j:
j = 2c + 3 = 2(17) + 3 = 37
Therefore, the price of the journal is $37 and the price of the cookbook is $17.
At Barnes and Noble, Sylvia purchased a journal and a cookbook that cost a total of $54, not including tax. If the price of the journal, j, is $3 more than 2 times the price of the cookbook, c, which system of linear equations could be used to determine the price of each item?
1. The equation for the total cost
2. The equation for the price of the journal
3. You can choose any method to solve this system: graphing, substitution, or elimination. Choose a method and solve for the price of the journal and the cookbook.
The price of the journal is
The price of the cookbook is
5 answers
Samuel currently has 18 rocks in his collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week.
Set up a system of equations to show how many rocks each has in their collection.
Samuel has y=Response areax+Response area.
Lewis has Response areax+Response area.
After how many weeks will Samuel and Lewis have the same number of rocks in their collections? Response area weeks
How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.
Set up a system of equations to show how many rocks each has in their collection.
Samuel has y=Response areax+Response area.
Lewis has Response areax+Response area.
After how many weeks will Samuel and Lewis have the same number of rocks in their collections? Response area weeks
How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.
Samuel: y = 18 + 4x
Lewis: y = 30 + 3x
To find the number of weeks it takes for them to have the same number of rocks, we can set the two equations equal to each other and solve for x:
18 + 4x = 30 + 3x
Simplify:
x = 12
Therefore, it will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.
To find how many rocks they will each have, we can substitute x = 12 into either equation:
Samuel: y = 18 + 4(12) = 66
Lewis: y = 30 + 3(12) = 66
Therefore, when they have the same number of rocks, they will each have 66 rocks in their collection.
Lewis: y = 30 + 3x
To find the number of weeks it takes for them to have the same number of rocks, we can set the two equations equal to each other and solve for x:
18 + 4x = 30 + 3x
Simplify:
x = 12
Therefore, it will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.
To find how many rocks they will each have, we can substitute x = 12 into either equation:
Samuel: y = 18 + 4(12) = 66
Lewis: y = 30 + 3(12) = 66
Therefore, when they have the same number of rocks, they will each have 66 rocks in their collection.
Samuel currently has 18 rocks in his collection and gains 4 each week. Lewis currently has 30 rocks in his collection and gains 3 each week.
Set up a system of equations to show how many rocks each has in their collection.
Samuel has y=Response areax+.
Lewis has Response areax+Response area.
After how many weeks will Samuel and Lewis have the same number of rocks in their collections? Response area weeks
How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.
Set up a system of equations to show how many rocks each has in their collection.
Samuel has y=Response areax+.
Lewis has Response areax+Response area.
After how many weeks will Samuel and Lewis have the same number of rocks in their collections? Response area weeks
How many rocks will Samuel and Lewis have when the amount of rocks in their collection is equal? They will each have Response area rocks in their collection.
Samuel: y = 18 + 4x
Lewis: y = 30 + 3x
To find the number of weeks it takes for them to have the same number of rocks, we can set the two equations equal to each other and solve for x:
18 + 4x = 30 + 3x
Simplify:
x = 12
Therefore, it will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.
To find how many rocks they will each have, we can substitute x = 12 into either equation:
Samuel: y = 18 + 4(12) = 66
Lewis: y = 30 + 3(12) = 66
Therefore, when they have the same number of rocks, they will each have 66 rocks in their collection.
Lewis: y = 30 + 3x
To find the number of weeks it takes for them to have the same number of rocks, we can set the two equations equal to each other and solve for x:
18 + 4x = 30 + 3x
Simplify:
x = 12
Therefore, it will take 12 weeks for Samuel and Lewis to have the same number of rocks in their collections.
To find how many rocks they will each have, we can substitute x = 12 into either equation:
Samuel: y = 18 + 4(12) = 66
Lewis: y = 30 + 3(12) = 66
Therefore, when they have the same number of rocks, they will each have 66 rocks in their collection.
7 answers