2009 AMC 8 Problems/Problem 1

Problem

Bridget bought a bag of apples at the grocery store. She gave half of the apples to Ann. Then she gave Cassie 3 apples, keeping 4 apples for herself. How many apples did Bridget buy?

$\textbf{(A)}\ 3\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 7\qquad\textbf{(D)}\ 11\qquad\textbf{(E)}\ 14$

Let us work backwards. We know that Cassie had 4 apples for herself at the end, and we know she gave away 3 apples before. Therefore, she had 7 apples before giving half of her original amount of apples to someone else. Since half of the amount of original apples is equal to seven, then the original amount of apples Bridget had is $7\cdot 2$ , giving us the answer $14$ , or $\boxed{E}$

Solution

We can work backwards to solve the problem. Bridget had 7 apples before she gave Cassie 3 apples. These 7 apples were half of Bridget’s 14 original apples. So the answer is .

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2009 AMC 8 Problems/Problem 1

Problem

Solution