Problem 10 · 2021 Math Kangaroo
Medium
Algebra & Patterns
substitution
The little kangaroo has chosen a special number. She gets the same result when she subtracts 110 from her number as she does when she multiplies it by 110. What is her number?
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Answer: E — 19
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Hint 1 of 2
Call the number x and write both described results as expressions.
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Hint 2 of 2
Set 'x minus 1/10' equal to 'x times 1/10' and solve.
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Approach: set the two described results equal
- Let the number be x. Subtracting gives x − 110; multiplying gives x10.
- Setting them equal: x − 110 = x10.
- Then 910x = 110, so x = 19.
- The number is 19, choice (E).
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