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.

Guest Jun 15, 2022

#1**+1 **

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

CPhill Jun 15, 2022

#2**+1 **

(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

Slimesewer Jun 16, 2022