Determining Amount of Salary X

Question

On Day 1 a girl spent 30 percent of her weekly pay X. On Day 2 she spent 60 percent of the remainder. If this left her with $1.00 less than the amount she spent on Day 1, what is the value of X?

Answer 1

PROBLEM

Determining Amount of Salary X

On Day 1 a girl spent 30 percent of her weekly pay X. On Day 2 she spent 60 percent of the remainder. If this left her with $1.00 less than the amount she spent on Day 1, what is the value of X?

SOLUTION

Day 0: Girl has weekly pay X

Day 1: Girl spends 30 percent of X; therefore, she has 70 percent of X remaining--0.70X

Day 2: Girl spends 60 percent of remainder; therefore, she has 40 percent left of the 70 percent she kept on Day 1--0.40*0.70X=0.28X--which is $1 less than the 30 percent she spent on Day 1. Thus, 0.28X = 0.30X-1.

Solving:

0.28X = 0.30X - 1

0.28X - 0.28X + 1 = 0.30X - 1 - 0.28X + 1

1 = 0.02X

1/0.02 = X

X = 50