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Algebra Difficulty 1.8 Junior Find the answer

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?

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

Solution

Since the average of three heights is 171 cm, then the sum of these three heights is 3 ×171 cm\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  cm\mathrm{~cm} - 161  cm\mathrm{~cm} = 352  cm.\mathrm{~cm}. Since Harpreet and Natalie are the same height, this height is 352 cm2\frac{352 \mathrm{~cm}}{2} = 176  cm.\mathrm{~cm}. Therefore, Natalie's height is 176 cm.

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