Problem 27 · 2020 Math Kangaroo
Stretch
Arithmetic & Operations
work-backwarddivision
Janaina bought three toys and spent all her money. For the first toy she paid half of her money plus 1 Real; for the second she paid half of what was left plus 2 Reais; for the third she paid half of what was left plus 3 Reais. How much money did she have to begin with?
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Answer: A — 34 Reais
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Hint 1 of 2
She ends with nothing, so undo the purchases from the last toy backward.
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Hint 2 of 2
Reverse each step: before a 'half plus k Reais' payment, the amount was (what was left + k) x 2.
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Approach: unwind the spending from the end
- After the third toy she has 0. That toy cost half of what she had plus 3, so before it she had (0+3)x2 = 6.
- Before the second toy (half plus 2): (6+2)x2 = 16.
- Before the first toy (half plus 1): (16+1)x2 = 34 Reais.
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