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Answer :
Final answer:
By setting up and solving a system of equations, it can be calculated that Alice bought 5 pounds of apples and 10 pounds of bananas.
Explanation:
Lets denote the pounds of apples Alice bought as 'a' and the pounds of bananas as 'b'. Since the problem mentions Alice bought twice as many pounds of bananas as she did apples, we can state that b = 2a.
The total cost of apples and bananas is $7.85, which given in cents becomes 785 cents. This can be written in equation form as 79a + 39b = 785.
Substitute 2a for b in the cost equation. This results in 79a + 39(2a) = 785, which simplifies to 79a + 78a = 785, and further simplifies to 157a = 785.
Solving for a, we divide both sides by 157, a = 785 ÷ 157 = 5. Therefore Alice bought 5 pounds of apples. And since b = 2a, we get b = 2 * 5 = 10. So Alice bought 10 pounds of bananas.
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