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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
avatar+124676 
+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

 

 

 

cool cool cool

 Jun 15, 2022
 #2
avatar+231 
+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

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