SOLUTION: William and his sister had a total of $520. After he spent 1/2 of his money and his sister spent 1/5 of her money, both of them still had the same amount of money left. a) How m

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Question 830768: William and his sister had a total of $520. After he spent 1/2 of his money and his sister spent 1/5 of her money, both of them still had the same amount of money left.
a) How much money did he spend?
b) How much money did his sister have left?
Thank you!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = amount William started with
Let +s+ = amount his sister started with
---------------
(1) +w+%2B+s+=+520+
(2) +w+-+%281%2F2%29%2Aw+=+s+-+%281%2F5%29%2As+
---------------------------
Multiply both sides of (2) by 10
(2) +10w++-+5w+=+10s+-+2s+
(2) +5w+=+8s+
(2) +w+=+%288%2F5%29%2As+
--------------------
By substitution:
(1) +%288%2F5%29%2As+%2B+s+=+520+
Multiply both sides by 5
(1) +8s+%2B+5s+=+2600+
(1) +13s+=+2600+
(1) +s+=+200+
and, since
(1) +w+%2B+s+=+520+
(1) +w+=+520+-+200+
(1) +w+=+320+
------------------
(a)
He spent +%281%2F2%29%2A320+=+160+
(b)
His sister has left +s+-+%281%2F5%29%2As+=+200+-+40+
+200+-+40+=+160+
--------------------
Check the answers:
(2) +w+-+%281%2F2%29%2Aw+=+s+-+%281%2F5%29%2As+
(2) +320+-+%281%2F2%29%2A320+=+200+-+%281%2F5%29%2A200+
(2) +320+-+160+=+200+-+40+
(2) +160+=+160+
OK