Question

4. John and Mitchell are buying snack from the break cart at school. John bought 2 bags of chips and 3

candy bars for $8.50. Mitchell bought 4 bags of chips and 2 candy bars for $11. How much did each item
cost?
Define your variables. x =
Write a system of equations.
Solve using any method.
y=_

Answer 1

Let's define the variables:
x = cost of 1 bag of chips
y = cost of 1 candy bar

With these definitions, the first equation for John's purchase can be written as:
2x + 3y = 8.50

The second equation for Mitchell's purchase can be written as:
4x + 2y = 11

Now we have a system of two equations:

2x + 3y = 8.50
4x + 2y = 11

To solve for x and y, we can use substitution or elimination method.

Let's use substitution method:
Solve for y in the first equation:
2x + 3y = 8.50
3y = 8.50 - 2x
y = (8.50 - 2x) / 3

Substitute this expression for y into the second equation:
4x + 2y = 11
4x + 2((8.50 - 2x) / 3) = 11
Expanding the right side:
4x + (17 - 4x) / 3 = 11
13x / 3 = 11 - (17 / 3)
13x / 3 = 11 - 5.67
13x / 3 = 5.33
Multiplying both sides by 3:
13x = 16
x = 16 / 13

So, the cost of 1 bag of chips is 16 / 13 dollars.

Substitute x = 16 / 13 into the expression for y:
y = (8.50 - 2x) / 3
y = (8.50 - 2(16 / 13)) / 3
y = (8.50 - 32 / 13) / 3
y = (8.50 - 2.46) / 3
y = 6.04 / 3
y = 2.02

So, the cost of 1 candy bar is 2.02 dollars