Question

After giving 1/3 of his money to his wife and 1/4 of it to his mother, Jake still had $600 left. How much money did he give to his mother?

Answer 1

Let's start by setting up an equation to represent the problem.

Let's say Jake started with x amount of money.

After giving 1/3 to his wife, he has 2/3 left: (2/3)x

After giving 1/4 of that amount to his mother, he has $600 left: (1/4)(2/3)x = $600

We can solve for x by isolating it:

(1/4)(2/3)x = $600

Multiplying both sides by 12/2 gives:

(2/3)x = $3600

Dividing both sides by 2/3 gives:

x = $5400

So Jake started with $5400.

To find out how much he gave to his mother, we can take 1/4 of 2/3 of $5400:

(1/4)(2/3)($5400) = $900

So he gave his mother $900.

Answer 2

Explanation:

x = original amount of money

the problem description tells us he gives 1/3 of his money to his wife and 1/4 of his money to his mother. and then he had still $600 left.

x - (1/3)x - (1/4)x = 600

so let's bring every fractional term to .../12.

12x/12 - (4/4)×(1/3)x - (3/3)×(1/4)x = 600

12x/12 - 4x/12 - 3x/12 = 600

5x/12 = 600

5x = 600×12

x = 600×12/5 = 120×12 = $1440

he gave to his mother

(1/4) × 1440 = $360