Question

1. julia and shawna are selling fruit for a school fundraiser. customers can buy small boxes of oranges and large boxes of oranges. julia sold 6 small boxes of oranges and 3 large boxes of oranges for a total of $99. shawna sold 1 small box of oranges and 3 large boxes of oranges for a total of $49. find the cost each of one small box of oranges and one large box of oranges. a) small box of oranges: $6, large box of oranges: $15 b) small box of oranges: $10, large box of oranges: $13 c) small box of oranges: $13, large box of oranges: $8 d) small box of oranges: $13, large box of oranges: $15 e) small box of oranges: $5, large box of oranges: $15

Explanation:

Step1: Define variables

Let \( x \) be the cost of a small box and \( y \) be the cost of a large box.
We have two equations:
\( 6x + 3y = 99 \) (from Julia's sales)
\( x + 3y = 49 \) (from Shawna's sales)

Step2: Subtract the second equation from the first

\( (6x + 3y) - (x + 3y) = 99 - 49 \)
Simplify: \( 5x = 50 \)

Step3: Solve for \( x \)

Divide both sides by 5: \( x = \frac{50}{5} = 10 \)

Step4: Substitute \( x = 10 \) into the second equation

\( 10 + 3y = 49 \)
Subtract 10: \( 3y = 49 - 10 = 39 \)

Step5: Solve for \( y \)

Divide by 3: \( y = \frac{39}{3} = 13 \)

Answer:

B) small box of oranges: $10, large box of oranges: $13