Question

Carlos and Shawn are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Carlos sold 13 small boxes of oranges and 5 large boxes of oranges for a total of $133. Shawn sold 10 small boxes of oranges and 8 large boxes of oranges for a total of $148. Find the cost of each of one small box of oranges and one large box of oranges.

Answer 1

Answer: The cost of one small box of oranges is $6, while the cost of one large box of oranges is $11.

Explanation:

First, set x for the cost of one small box of oranges in dollars, and y for the cost of one large box of oranges in dollars.

Hence, the equations will be:

`13x+5y=133`

`10x+8y=148`

Then solve for the equations using the method of elimination. In order to eliminate one of the variables, you need to make the coefficients the same. So, we can multiply the first equation by 8 and the second equation by 5. That would make the equations:

`104x+40y=1064`

`50x+40y=740`

Then you can eliminate the y by subtracting.

`54x = 324`

Then divide by 54 on both sides.

`x=6`

Now that x is solved, solve for y by substituting for x.

`13(6) + 5y = 133`

`5y+78=133`

`5y=55`

`y=11`

So, x=6 and y=11.