Question

Kyle gave 2/7 of his money to his wife and spent 3/5 of the remainder. If he had $300 left, how much money did he have at first?

Answer 1

Kyle gave 2/7th of his money to his wife and spent 3/5 of the remainder. If he had $300 left, the money had by Kyle at first is $1050

Solution:

Step 1:

Consider “x” as the money which Kyle had initially.

From question, Kyle gave 2/7th of his money to his wife. So the remaining money left with Kyle is given as,

`= 1 - (2)/(7)`

`= (7 - 2)/(7) = (5)/(7)` ----- eqn 1

Now the remaining money left with Kyle is 5/7th.Given that Kyle spent 3/5 of the remaining money.

Now the remaining money left with Kyle is given as

`= 1 - (3)/(5) = (5 - 3)/(5) = (2)/(5)`

Now kyle is left with $300, which is 2/5th of the initial money x .

We get equation as

`(2)/(5) x=300`

2x = 1500

x = 750

Now Kyle is left with 750$ which is 5/7th of the initial amount x.( by using eqn 1)

We get equation as

`(5)/(7) x = 750`

5x = 5250

x = 1050

So the amount had by Kyle at first is $1050