Find the cost of 1 large box and 1 small box

Question

Lisa sold 4 small boxes of grapefruit and 5 large boxes of Grapefruit for a total of $105. Nicole sold 8 small boxes of grapefruit and 1 large box of for a total of $57. Find the cost of 1 small box of grapefruit and 1 large box of grapefruit.

Answer 1

This is a systems of equations problem. We need to create two equations from the information given to us, and then solve the system of equations.

Let small boxes be represented by x, and large boxes be represented by y.

4x + 5y = 105

8x + y = 57

The second equation lends itself to substitution, as follows:

8x + y = 57

-8x -8x

y = 57 -8x

Then, we can substitute for y in the first equation

4x + 5(57-8x) = 105

4x + 285 - 40x = 105

-36x + 285 = 105

-285 -285

-36x = -180

-36 -36

x = 5

Then, we can substitute our answer for x back into one of the original equations to find y. Let's use the second one:

8x + y = 57

8(5) + y = 57

40 + y = 57

-40 -40

y = 17

So, 1 small box costs $5, and one large box costs $17

We can verify this by plugging these numbers back into the original equation:

4x + 5y = 105

4(5) + 5(17) = 105