Terry, Carl and Dave bought a present for their friend. Terry paid 1/3 of the total amount paid by Carl and Dave. Carl paid 2/5 of the amount paid by Terry and Dave. If Terry paid $24 less than Dave for the present, find the cost of the present.
Let the amount that Terry paid = P
Let the amount that Dave paid = P + 24
The amount that Carl paid = (2/5) ( P + P 24) → (2/5) (2P + 24)
So....the amount that Terry paid = (1/3) (2/5) ( 2P + 24)
So
P = (1/3) [ (2/5)(2P + 24) + ( P + 24) ] multiply both sides by 3
3P = (2/5) (2P + 24) + ( P + 24) multiply through by 5
15P = 2 (2P + 24) + 5 ( P + 24)
15P = 4P + 48 + 5P + 120
15P - 4P - 5P = 48 + 120
6P = 168
P = 168 / 6 = 28 = what Terry paid
P + 24 = 52 = what Dave paid
(2/5) ( 28 + 52) = (2/5) (80) = 32 = what Carl paid
The present cost 28 + 52 + 32 = $112
