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Twenty children were sharing equally the cost of a present f

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Founder
Joined: 18 Apr 2015
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Twenty children were sharing equally the cost of a present f [#permalink]  23 Jan 2019, 16:13
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Question Stats:

85% (01:46) correct 14% (01:46) wrong based on 14 sessions
Twenty children were sharing equally the cost of a present for their teacher. When 4 of the children decided not to contribute, each of the other children had to pay \$1.50 more. How much did the present cost, in dollars? ​

A. 50 ​

B. 80 ​

C. 100 ​

D. 120 ​

E. 150
[Reveal] Spoiler: OA

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Intern
Joined: 07 Jan 2019
Posts: 38
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Kudos [?]: 21 [1] , given: 11

Re: Twenty children were sharing equally the cost of a present f [#permalink]  27 Jan 2019, 07:20
1
KUDOS
Solution,

Let the present cost, in dollars be x.

the share of each child by y.

According to the question,

We can set two equations as follows:

20y = x..............equation 1

16y + 16 * 1.50 = x

or, 16 y + 24 = x.....equation 2

Solving equation 1 & 2,

16 * x/20 + 24 = x

or, 16x/20 + 24 = x

or, 16x + 480 = 20x

or, 4x = 480

or, x = 120

Thus, the answer is D.
Intern
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Re: Twenty children were sharing equally the cost of a present f [#permalink]  07 Feb 2019, 10:08
Carcass,

Can you please provide the O.E?

Thanks!
Founder
Joined: 18 Apr 2015
Posts: 7737
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Kudos [?]: 1593 [1] , given: 7026

Re: Twenty children were sharing equally the cost of a present f [#permalink]  07 Feb 2019, 11:34
1
KUDOS
Expert's post
Quote:
Let x be the amount in dollars that each of the 20 children were going to contribute; then 20x represents the cost of the present.

When 4 children dropped out, the remaining 16 each had to pay (x + 1.50) dollars. So, 16(x + 1.5) = 20x ⇒ 16x + 24 = 20x ⇒ 24 = 4x ⇒ x = 6, and so the cost of the present was 20 × 6 = 120 dollars.

Alternative Solution.

Since each of the 16 remaining children had to pay an extra \$1.50, the extra payments totaled 16 × \$1.50 = \$24. This is the amount that would have been paid by the 4 children who dropped out, so each of the 4 would have paid \$6. The cost of the gift was 20 × \$6 = \$120.

Hope is clear.

Ask for further assistance.

Regards
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Re: Twenty children were sharing equally the cost of a present f [#permalink]  27 May 2019, 12:40
1
KUDOS
Carcass wrote:
Twenty children were sharing equally the cost of a present for their teacher. When 4 of the children decided not to contribute, each of the other children had to pay \$1.50 more. How much did the present cost, in dollars? ​

A. 50 ​

B. 80 ​

C. 100 ​

D. 120 ​

E. 150

4 children left ------> cost increased by \$1.5 for each of 16 children.

So, total increase is 1.5*16 = \$24

this \$24 was earlier contributed by 4 children who backed out i.e on average they were contributing \$6 each

This \$6 was average for all children which now has increased by \$1.5 i.e new average is 7.5 for 16 children
So, net cost of present is 7.5*16 or 6*20 = \$120
Re: Twenty children were sharing equally the cost of a present f   [#permalink] 27 May 2019, 12:40
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