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# Help

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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.

Jun 15, 2022

#1
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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

Jun 15, 2022
#2
+237
+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

Jun 16, 2022