CEMC Cayley

Algebra Difficulty 2.4 Junior Find the answer

Consider the following flowchart: INPUT $\rightarrow$ Subtract $8 \rightarrow \square \rightarrow$ Divide by $2 \rightarrow \square$ Add $16 \rightarrow$ OUTPUT. If the OUTPUT is 32, what was the INPUT?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

We start from the OUTPUT and work back to the INPUT. Since the OUTPUT 32 is obtained from adding 16 to the previous number, then the previous number is $32 - 16 = 16$ . Since 16 is obtained by dividing the previous number by 2, then the previous number is $2 \times 16$ or 32. Since 32 is obtained by subtracting 8 from the INPUT, then the INPUT must have been $32 + 8 = 40$ .

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