Question

5 kids have an average weight of 50 pounds. Jim is the heaviest kid, while Tim is the lightest. If Jim is excluded, the average becomes 40 pounds, and if Tim is excluded, the average becomes 60 pounds. What is the average weight of Jim and Tim?

Answer 1

Let the weights of the 5 kids be W1, W2, W3, W4, and W5, with Jim weighing W5, and Tim weighing W1.

It is given that:

The average weigth of all the kids is
$\frac{\text{sum of the weights of all the kids}}{\text{number of kids}}$

$\frac{\text{W1 + W2 + W3 + W4 + W5}}{5}=50$

W1 + W2 + W3 + W4 + W5 = 50 $\times$ 5

W1 + W2 + W3 + W4 + W5 = 250 pounds

If we exclude W5, then:

$\frac{\text{W1 + W2 + W3 + W4}}{4}=40$

W1 + W2 + W3 + W4 = 40 $\times$ 4

W1 + W2 + W3 + W4 = 160 pounds

From this, we can say that:
W5 = 250 – 160 = 90 pounds

If we exclude W1, then:

$\frac{\text{W2 + W3 + W4 + W5}}{4}=60$

W2 + W3 + W4 + W5 = 60 $\times$ 4

W2 + W3 + W4 + W5 = 250 pounds

From this, we can say that:
W1 = 250 – 240 = 10 pounds

The average of W1 and W5 is:

$\frac{\text{W1 + W5}}{2}=\frac{\text{10 + 90}}{2}$

$=\frac{\text{100}}{2}=50pounds$