Problem 5 · 2007 AMC 8
Easy
Arithmetic & Operations
target-amount
Chandler wants to buy a 500 dollar mountain bike. For his birthday, his grandparents send him 50 dollars, his aunt sends him 35 dollars and his cousin gives him 15 dollars. He earns 16 dollars per week for his paper route. He will use all of his birthday money and all of the money he earns from his paper route. In how many weeks will he be able to buy the mountain bike?
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Answer: B — 25 weeks.
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Hint 1 of 2
The gift money is a head start — subtract it first so only the paper-route money has to close the gap. Don't make the weekly route 'pay' for what's already in hand.
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Hint 2 of 2
Gap ÷ rate: figure out how much is still missing, then divide by the per-week amount.
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Approach: close the remaining gap at the weekly rate
- Birthday head start: 50 + 35 + 15 = 100. That shrinks the goal to 500 − 100 = 400 left to earn.
- Each week the route adds 16, so weeks = 400 ÷ 16 = 25.
- Pattern to keep: 'how long to reach a goal' is almost always (goal − what you already have) ÷ (rate per step). Knock out the head start before dividing.
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