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.
+129852 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
+237 (1) T = 1/3 (C + D)
(2) C = 2/5 (T + D)
(3) T = D - 24
D - 24 = 1/3 (C + D)
3D - 72 + C + D
C = 2D - 72
C = 2/5 (D - 24 + D)
C = 2/5 (2D - 24
2D - 72 = 2/5 (2D - 24)
5D - 180 = 2D - 24
3D = 156
Dave = $52
T = 52 x 24
Terry = $28
C = 2 (52) - 72
Carl = $32
The present cost = 52 + 28 + 32
= $112
