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Question

Four girls, Alice, Betty, Cher and Debra shared the cost of a present equally. Cher had some money but she did not have enough to pay for her share. Alice paid more to make up for the difference for Cher. The amount paid by Alice is 1/2 of what Betty, Cher and Debra paid in total. Cher returned $40 to Alice in the end. Find the cost of the present.

Answer

Let the cost of present = 4 x (1 unit + 40) = 4 units + 160
Alice : 1 unit + 80
Betty, Cher & Debra : 3 units + 80
3 units + 80 = (1 units + 80) x 2 = 2 units + 160
1 units = 80
4 units + 160 = 4 x 80 + 160 = 480

Ans : $480.

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Let Cher’s share be U
Alice’s share U+40+40 = U+80

Betty’s share U+40

Debra’s share U+40

Cher, Betty & Debra’s share =
U+U+40+U+40 = 3U+80

2x Alice’s share = Cher, Betty & Debra’s share
2(U+80) = 3U + 80
2U+160 = 3U + 80
U = 80

Price of the present = 4x U+$40
= 4x $80+$40
= 4x $120
= $480

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