Natalie and Harpreet are the same height. Jiayin's height is 161 cm. The average (mean) of the heights of Natalie, Harpreet and Jiayin is 171 cm. What is Natalie's height?
Solution
Since the average of three heights is 171 cm, then the sum of these three heights is 3 \times 171 \mathrm{~cm} or 513 cm. Since Jiayin's height is 161 cm, then the sum of Natalie's and Harpreet's heights must equal 513 \mathrm{~cm} - 161 \mathrm{~cm} = 352 \mathrm{~cm}. Since Harpreet and Natalie are the same height, this height is \frac{352 \mathrm{~cm}}{2} = 176 \mathrm{~cm}. Therefore, Natalie's height is 176 cm.
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