Question

John took all his money from his savings account. He spent $52 on a radio and 1/2 of what was left on presents for his friends, Of the money remaining, John put 4/13 into checking account and the last remaining $180 was left to charity. How much money did John originally have in his savings account?

Answer 1

Answer:

John had $572 in his savings account.

Step-by-step explanation:

Let the total amount John took from his savings account be T.

He spent $52. That means he has $(T - 52) left.

He then spent 1/2 of what was left on presents for his friends. That is:

$\frac{1}{2} * (T - 52) = \frac{T - 52}{2}$

Which means he is left with another half of what was left, that is, $\frac{T - 52}{2}$

Of the money remaining, John put 4/13 into checking account.

This means that he is left with 9/13 of $\frac{T - 52}{2}$.

We are told that this is equivalent to the last remaining $180 that John left to charity.

=> $\frac{9}{13} * \frac{T - 52}{2} = 108$

Hence:

$\frac{9(T - 52)}{13 * 2} = 180\\\\9(T - 52) = 180 * 13 * 2\\\\9(T - 52) = 4680\\\\T - 52 = \frac{4680}{9} = 520$

=> T = 520 + 52 = $572

Hence, John took $572 from his savings account. Since this is all he had in his savings account, John had $572 in his savings account.