# Aminah, Banu, and Chen went shopping during the great Singapore sale. The ratio of the amount Aminah spent to the amount spent by Banu and Chen is 3:5. The ratio of the amount Banu spent to the amount spent by Aminah and Chen is 1:4. Banu spent 85.50 less than Chen. How much did Aminah spend?

Posted by Anonymous on

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A/(b+c) = 3/5
b/(a+c) = 1/4
c-85.5 = b
so
a/(2c-85.5) = 3/5
(c-85.5)/(a+c) = 1/4
so
5a = 3(2c-85.5) = 6c-256.5
4(c-85.5) = a+c
4c-342 = a+c
so
a = 3c-342
so
5(3c-342) = 6c-256.5 = 15c-1710
so
15c-6c = 1710-256.5
c = 161.5
a = 3*161.5 - 342 = 142.5
b = 161.5-85.5 = 76
Check
a/(b+c) = 0.6 = 3/5

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