John took all his money out of his bank savings account. He spent $35 on a radio

Question

John took all his money out of his bank savings account. He spent $35 on a radio and 3/5 of what remained on gifts. After gifts were purchased, 1/3 of what was left was put back in his checking account, and the remaining $24 was donated to charity. How much money did John have originally in his savings account?

Here is a similar question and how it was worked out::

John took all his money out of his bank savings account. He spent $20 on a radio and 2/3 of what remained on gifts. After gifts were purchased, ¾ of what was left was put back in his checking account, and the remaining $20 was donated to charity. How much money did John have originally in his savings account?

Problem 02

G

G

G

G

G

G

G

G

C

C

C

1 white square must be worth $20.

The whole rectangle should be worth $20´12 = $240. Originally he must have had

$240+$20 = $260.

Explanation / Answer

Let us assume that John had $x originally in his savings account.

He took all his money out of his bank savings account.

He spent $35 on a radio and 3/5 of what remained on gifts.

So, expenses on gifts was (3/5)*(x – 35) = 3(x – 35)/5

After purchase of radio and gifts, balance left = x – 35 – 3(x – 35)/5

= (x – 35)(1 – 3/5) = (x – 35)(2/5) = (2/5)(x – 35)

Therefore, amount deposited in checking account = (1/3)* (2/5)(x – 35)

= (1/3)(2/5)(x – 35) = (2/15)(x – 35)

Balance left after depositing money into the checking account = (2/5)(x – 35) – (2/15)(x – 35)

= (2/5 – 2/15)(x – 35)

= 2/5(1 – 1/3)(x – 35)

= (2/5)(2/3)(x – 35)

= (4/15)(x – 35)

This is the amount that was donated to charity. Therefore,

(4/15)(x – 35) = 24

(x – 35) = 24*(15/4)

x – 35 = 90

x = 35 + 90 = 125

Therefore, John had $125 originally in his savings account. (Answer)

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