Step-5

Title: Averages

Grade: 8-a Lesson: S3-L2

Explanation: Let us verify the answer here with the steps.

Description:

Step Type Explanation Answer

1

Problem

The average weight of P, Q, and R is 60 kg. The weight of Q is 20 kg less than P’s weight and R’s weight is 25 kg less than P’s weight. What will be the average of P, Q, R, and S if S weighs 2 kg more than R?

2

Hint

Formula used

\$"Average" = "Sum of set of numbers" / "Amount of numbers in set"\$

3

Step

Average weight of P, Q and R

60kgs

4

Step

On Simplification

\$(P + Q + R)/3 = 60\$

5

Step

On Cancellation

\$P + Q + R = 60 \times 3 = 180\$ → (1)

6

Step

Let "x" be the weight

7

Step

According to the problem,

P = x, Q = x - 20, R = x - 25 → (2)

8

Step

Substitute

the values in equation(1)

9

Step

On Cancellation

\$x + x - 20 + x - 25 = 180\$

10

Step

On Cancellation

\$3x= 180 + 45 = 225\$

11

Step

On Cancillation

\$x= 225/3 = 75\$

12

Step

Substituting x in equation(2)

P = 75, Q = 55, R = 50

Since S is 2 more than R then S = 52


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