SOLUTION: Twenty children are sharing equally the cost of a present. 4 of the children decide not to contribute, each of the other children had to pay $1.50 more. How much did the present

Question 1161770: Twenty children are sharing equally the cost of a present. 4 of the children decide not to contribute, each of the other children had to pay $1.50 more.
How much did the present cost, in dollars?
Found 3 solutions by jim_thompson5910, MathTherapy, greenestamps:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

p = cost of present in dollars
p/20 = cost each person chips in if there are 20 people paying their fair share

Four people decide to drop out, so there are 16 people left.
The cost per person is now p/16. This is increased by $1.50, so,
p/16 = (p/20)+1.50
p/16 - p/20 = 1.50
20p/320 - 16p/320 = 1.50
4p/320 = 1.50
p/80 = 1.50
p = 80*1.50
p = 120 is the cost of the present

Let's see if we got the right answer.
If the present was p = 120 dollars, then twenty people will pay p/20 = 120/20 = 6 dollars each.
If four of them decide not to participate, then sixteen people will pay p/16 = 120/16 = 7.50 dollars each.
Each person pays 7.50 - 6.00 = 1.50 more dollars, which matches with what the instructions state.
The answer is confirmed.

Answer: the present costs $120

Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!
Twenty children are sharing equally the cost of a present. 4 of the children decide not to contribute, each of the other children had to pay $1.50 more.
How much did the present cost, in dollars?

Let cost of present be P
Then each child pays
With 4 children dropping out, each of the remaining 16 (20 - 4) children will then pay,
We then get:
4P = 5P - 1.5(80) ------ Multiplying by LCD, 80
4P - 5P = - 1.5(80)
- P = - 1.5(80)
Cost of present, or
Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!

Two other tutors have shown algebraic solutions using the cost of the present as the variable.

Here is a very different solution method....

let x = cost per person when there are 20 children
then x+1.50 = cost per person when there are 20-4 = 16 children

The cost is the same either way:

The cost per person is $6 when there are 20 children; so the cost of the present is 20($6) = $120.

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