Question

# There are 8 people in the lift. Few are ladies and the rest are children. Each lady weighs 150 pounds. Each child weighs 50 pounds. The total weight of the 8 people is 800 pounds. Construct the system of linear equations and use elimination method to solve.

Hint:

### let the no. of ladies in the lift be x and let the number of children be y

Given total no. of people = no. of ladies + no. of children = 8

Given total weight = weight of x ladies + weight of y children = 800.

## The correct answer is: 4

### Ans :- The no. of ladies in the lift are 4 and no. of children in the lift are 4 .

Explanation :-

Step 1:- construct the system of linear equations

let the no. of ladies in the lift be x and let the number of children be y

Given total no. of people = no. of ladies + no. of children = 8

So, x + y = 8 — eq1

Given total weight = weight of x ladies + weight of y children = 800.

weight of x ladies = x weight of each lady ( Each lady weighs 150 pounds)

weight of x ladies = 150x (pounds)

weight of y children = y weight of each child ( Each child weighs 50 pounds)

weight of y children = 50y (pounds)

So total weight = 150x + 50y = 800 — eq2

Step 2 :- eliminate x to find value of y

Doing eq2 - 150 eq1 to eliminate x

We get 150x + 50y - 150 (x + y) = 800 - 150(8)

∴ y = 4

Step 3:- substitute the value of y in eq1 to get the value of x

∴ x = 4

∴The no. of ladies in the lift are 4 and no. of children in the lift are 4 .

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