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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