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

Answer:

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,

$= 1 - \frac{2}{7}$

$= \frac{7 - 2}{7} = \frac{5}{7}$ ----- 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  

$= 1 - \frac{3}{5} = \frac{5 - 3}{5} = \frac{2}{5}$

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

We get equation as  

$\frac{2}{5} x=300$

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

$\frac{5}{7} x = 750$

5x = 5250

x = 1050

So the amount had by Kyle at first is $1050