+16 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?
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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)
Check answers
(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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