1999 CEMC Gauss (Grade 7) Problems/Problem 18

Problem

The results of the hair colour of $600$ people are shown in this circle graph. How many people have blonde hair?

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$\text{(A)}\ 30 \qquad \text{(B)}\ 160 \qquad \text{(C)}\ 180 \qquad \text{(D)}\ 200 \qquad \text{(E)}\ 420$

Solution 1

The total percentage should add up to $100\%$ , so the total percentage of individuals with blonde hair can be found by finding the total percentage of people with other hair colors, and subtracting the total from $100\%$ .

This gives: $100\% - (32\% + 22\% + 16\%) = 30\%$

This means $30\%$ of the $600$ individuals shown in the results had blonde hair, which means:

$30\% \times 600 = 600 \times \frac{30}{100} = \boxed {\textbf {(C)} 180}$

Solution 2

We can find the total number of people that have each hair color, outside of blonde hair. This gives:

$32\% \times 600 + 32\% \times 600 + 16\% \times 600 = 32 \times 6 + 32 \times 6 + 16 \times 6 = 420$

To find the number of blonde hair individuals, we can then subtract this from the total number of people. We then get:

$600 - 420 = \boxed {\textbf {(C) } 180}$

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1999 CEMC Gauss (Grade 7) Problems/Problem 18

Problem

Solution 1

Solution 2