Question

The average weight of 3 boys is 53 pounds. Not one of these boys weights less than 51 pounds. What is the maximum weight, in pounds, of any one boy? A. 53 B. 55 C. 57D. 59

Answer 1

The average weight of 3 boys is 53 pounds. We know that none of them weighs less than 51 pounds, and we need to know the maximum weight of any of them. If the weights are w1, w2, and w3, taking the average:

`\begin{gathered} (w_1+w_2+w_3)/(3)=53 \\ w_1+w_2+w_3=3\cdot53 \\ w_1+w_2+w_3=159 \end{gathered}`

Let's say that the third boy has the maximum weight. Then:

`w_3=159-w_2-w_1`

To make it the maximum, w2 and w1 should be the minimum, and we know that none of them weighs less than 51, so the minimum is 51. Then:

`\begin{gathered} w_1=51 \\ w_2=51 \\ \Rightarrow w_3=159-51-51 \end{gathered}`

Finally:

`w_3=57\text{ pounds}`

The maximum weight is 57 pounds.