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# Algebra

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Kaspar is buying apples and oranges from the market. The total cost of 4 apples and 3 oranges is \$11, while the total cost of 2 apples and 5 oranges is \$13. What is the cost of each apple and each orange?

Nov 16, 2023

#2
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Kaspar is buying apples and oranges from the market. The total cost of 4 apples and 3 oranges is \$11, while the total cost of 2 apples and 5 oranges is \$13. What is the cost of each apple and each orange?

4A + 3G  =  11     (eq 1)

2A + 5G  =  13     (eq 2)

Multiply (eq 2) by 2                    4A + 10G  =  26   (eq 3)

Subtract (eq 1) from (eq 3)                  7G  =  15

G  =  15 / 7  =  2.14   (one orange)

Plug the value of an orange

back into (eq 1)                          4A + (3)(2.14)  =  11

4A  =  11 – 6.42  =  4.58

A  = 4.58 / 4  =  1.14   (one apple)

(eq 1)                            4 • (1.14) + 3 • (2.14)  =  10.98   close enough to 11

(eq 2)                            2 • (1.14) + 5 • (2.14)  =  12.98   close enough to 13

The answers check out, considering that the calculations required rounding.

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Nov 17, 2023