YY has $130 more than her sister ZZ. ZZ had 2X as much $ as their younger sister WW. If their mother gave YY $60 and ZZ $80. YY would have 2X as much $ as ZZ. What was the total amount of $ they had at the start?

YY begins with $130 more than ZZ who has double WW. The crucial part is that when $60 is added to YY, and $80 to ZZ, YY has twice ZZ. This gives us enough factors to play around with some numbers.

Let's start with something simple. Say ZZ has $100. This would of course put YY on $230 and WW on $50. How does this work out if we add in the new amounts?

YY: $230 + $60 = $ 290

ZZ: $100 + $80 = $180

YY clearly doesn't have double ZZ at the end; in fact, we're quite a way off. The ZZ amount is too high (or YY is too low). Let's try again with some lower numbers.

Let's say YY has $150. This means ZZ would have $20 and WW on $10. Do these numbers get closer to what we want?

YY: $150 + $60 = $210

ZZ: $20 + $80 = $100

We're only $10 out now if we're looking for YY's final sum to be twice ZZ. Maybe if we increased the initial figures for YY by $10, we might have something:

YY: $160 + $60 = $220

ZZ: $30 + $80 = $110

We've found it! We've added in the new figures as asked, and we can see $220 is twice $110. All we need to do is work backwards a little for WW's starting figure, which was half of what ZZ started with:

WW = $30 divided 2 = $15

Therefore, YY began with $160, ZZ with $30 and WW with $15.