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The remaining money after spending $49 on dress is the box with blue border. As 2/5 of it is spent on shoes, we can write it as 2u vs 3u. Working: Dress = 49 Shoes = 2u (2/5 of remaining) Left = 3u (is also 1/4 of total) Amount left = 3u = 1/4 of total. So total is 4 x 3u = 12u. Thus Dress is 12u - 5u = 7u = 49 and u = 7. So Mary had 12u = 12 x 7 = $84 at first. Check: Remaining after dress: 84 - 49 = 35 Shoes = 2 x 7 = 14 and 14/35 = 2/5. Left = 35 - 14 = 21 and 21/84 = 1/4.
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Let u be the total money at first.
[ Dress ][ Shoes ][ Left ]
[ ——49——-][——(2/5)(u-49)——–][—–1/4u—]
[——————-(3/4)u———————]
49 + (2/5)(u-49) = (3/4)u ( x 20 on both sides)
980 +8(u-49) = 15u
7u = 980-392 = 588
u = 588/7 = 84
Hence Mary has $84 at first.
waterflow
The key point to solve this problem is to be very clear of 2/5 and ¼ are referring to different amount of money.
2/5 is referring to remaining money which is ( sum of money-49 ) and ¼ is referring to the sum of money.
Let the sum of Money be S.
S – 2/5*(S-49) – 49= ¼*S
S*(1-2/5-1/4)=49*3/5
7/20*S=49*3/5
S=84
So the sum of money is $84.