John spent $70 and 2/5 of what was left. John then put 4/7 into achecking and donated the $180 that was left to charity. How much did John originally have?

Question

I need to know how much John originally had in his savings

Answer 1

Let A be the amount John started with. According to the problem, the sequence of events was:

 

John spent $70, (A - 70)

John spent 2/5 of (A - 70)

John deposited 4/7 of what was left after his spending, A - 70 - 2/5(A - 70)

John deposited $180, the amount that was left over after the spending and the deposit

 

180 = 4/7(A - 70 - [2/5(A - 70)]) -- Set up the equation

180 = 4/7(A - 70 - 2A/5 + 28) -- Distribute the 2/5

180 = 4A/7 - 40 - 8A/35 + 16 -- Distribute the 4/7

180 = 4A/7 - 8A/35 - 24 -- Simplify

204 = 20A/35 - 8A/35 -- Add 24 to both sides and multiply first term on the right by 5/5 to get common denominators

12A/35 = 204 -- Simply and rewrite

12A = 7140 -- Multiply both sides by 35 and then divide both sides by 12.

A = 595

 

John began with $595.