Question

A school sold small and large boxes of fruit as a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Let x represent the price of a small box and y represent the price of a large box. Solve the system to determine the price of each size box of fruit. Negative 12 (5 x 13 y = 323) right-arrow negative 60 x minus 156 y = negative 2,784 5 (12 x 7 y = 218) right-arrow 60 x 35 y = 1,090 The price of a small box of fruit is $10 and the price of a large box of fruit is $14. The price of a small box of fruit is $8 and the price of a large box of fruit is $14. The price of a small box of fruit is $10 and the price of a large box of fruit is $16. The price of a small box of fruit is $14 and the price of a large box of fruit is $16.

Answer 1

The price of a small box of fruit is $10 and the price of a large box of fruit is $14.]

Given

A school sold small and large boxes of fruit as a fundraiser.

One student sold 5 small boxes and 13 large boxes for $232.

Another student sold 12 small boxes and 7 large boxes for $218.

Let, x represent the price of a small box and y represent the price of a large box.

One student sold 5 small boxes and 13 large boxes for $232.

$\rm 5x+13y=232$

Another student sold 12 small boxes and 7 large boxes for $218.

$\rm 12x+7y=218$

From equation 1

$\rm 5x+13y=232\\\\5x=232-13y\\\\x=\dfrac{232-13y}{5}$

Substitute the value of x in equation 2

$\rm 12x+7y=218\\\\12\times \dfrac{232-13y}{5}+7y=218\\\\2784-156y+35y=218\times 5\\\\2784-121y=1090\\\\-121y=1090-2784\\\\-121y=--1694\\\\y=\dfrac{-1694}{-121}\\\\y=14$

Substitute the value of y in equation 1

$\rm 5x+13y=232\\\\5x+13(14)=232\\\\5x+182=232\\\\ 5x=232-180\\\\5x=50\\\\x=\dfrac{50}{5}\\\\x=10$

Hence, The price of a small box of fruit is $10 and the price of a large box of fruit is $14.

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Answer 2

Answer:

A-The price of a small box of fruit is $10 and the price of a large box of fruit is $14.

Step-by-step explanation: