Problem 13 · 2010 Math Kangaroo
Medium
Algebra & Patterns
work-backward
Benjamin chooses a number, divides it by 7, adds 7 to the result, and then multiplies that result by 7. He obtains the number 777. Which number did he start with?
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Answer: E — 728
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Hint 1 of 2
Run the story backwards, starting from the final answer 777.
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Hint 2 of 2
Each step undoes the one Benjamin did: undo a multiply with a divide, undo an add with a subtract.
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Approach: undo each step from the end
- The last thing he did was \(\times 7\), so undo it: \(777 \div 7 = 111\).
- Before that he added 7, so undo it: \(111 - 7 = 104\).
- The first thing he did was \(\div 7\), so undo it: \(104 \times 7 = 728\) — the answer is E.
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