SOLUTION: Darrell has $2 less than five times as much money as Bob. Mary has as much money as Darrell ans Bob together. If all three of them together have $80, how much does Mary have?

Question 500868: Darrell has $2 less than five times as much money as Bob. Mary has as much money as Darrell ans Bob together. If all three of them together have $80, how much does Mary have?
Answer by geetha_rama(94) (Show Source): You can put this solution on YOUR website!
Let x be the amount that Darell have. y be the amount that Bob have and z be the amount that Mary have.
x + y + z = 80 -> equation 1 (All three of them have $80 in total)
x = 5y -2 -> equation 2 (Darell has $2 less than five times the money bob have)
z= x+y -> equation 3 (Mary has sum of Darell and Bob's money)
substituting equation 3 in equation 1,
we have
x + y + x+ y = 80
2x + 2y = 80
=> x+y=40
x-5y = -2 ( from equation 2)

subraticting above two equations,
-6y = -42
=> y = 7
x = 5y -2 = 35 -2 = 33
Z = x+y = 40
Darell has $33, Bob has $7 and Mary has $40

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