Question 96524: A, b, c, d, and e went shopping. Each had a whole number of dollars to spend, and together the had $56. The absolute difference between the amounts that a and b had to spend was $19; between c and b, $7; between c and d, $5; between d and e $4. and between e and a $11. how much did e have to spend
please explain
Answer by psbhowmick(878)   (Show Source):
You can put this solution on YOUR website! Assume that A spend $a, B spend $b, C spend $c, etc.
So, a + b + c + d + e = 56 ___________ (1)
a - b = 19 or a = b + 19 ______ (2)
c - b = 7 or c = b + 7 ______ (3)
c - d = 5 or d = c - 5 = (b + 7) - 5 = b + 2 [from the above equation] ______ (4)
d - e = 4 or e = d - 4 = (b + 2) - 4 = b - 2 [from the above equation] ______ (5)
Substituting the values of a, c, d, e in terms of b in (1)
(b + 19) + b + (b + 7) + (b + 2) + (b - 2) = 56
5b + 26 = 56
5b = 56 - 26 = 30
b = 30/5 = 6
So, e = b - 2 = 6 - 2 = 4
Hence, E spent $4.
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