2015 CEMC Gauss (Grade 8) Problems/Problem 8

Problem

At the beginning of the summer, Aidan was 160 cm tall. At the end of the summer, he measured his height again and discovered that it had increased by $5\%$ . Measured in cm, what was his height at the end of summer?

$\textbf{(A)}\ 168 \qquad\textbf{(B)}\ 165 \qquad\textbf{(C)}\ 160.8 \qquad\textbf{(D)}\ 172 \qquad\textbf{(E)}\ 170$

Solution 1

Let $x$ be the number of centimeters that Aidan's height increased, and $h$ be his height after the summer. Using the fact that his original height was $160$ and his height increased by $5\%$ of that, we have:

$x = 5\% \times 160 = \frac{1}{20} \times 160 = 8 \text{cm}$

$h = x + 160 = 8 + 160 = \boxed {\textbf {(A) } 168} \text{cm}$

~anabel.disher

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2015 CEMC Gauss (Grade 8) Problems/Problem 8

Problem

Solution 1