SOLUTION: here were 429 people at a play. Admission was S1 each for adults and 75 cents each for children. The receipts were S372.50. How many children and how many adults attended?

Question 1198535: here were 429 people at a play. Admission was S1 each for adults and 75
cents each for children. The receipts were S372.50. How many children and
how many adults attended?
Found 3 solutions by Alan3354, MathTherapy, greenestamps:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
here were 429 people at a play. Admission was S1 each for adults and 75
cents each for children. The receipts were S372.50. How many children and
how many adults attended?
------------------------
A + C = 429
100A + 75C = 37250

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

here were 429 people at a play. Admission was S1 each for adults and 75
cents each for children. The receipts were S372.50. How many children and
how many adults attended?

Let number of adults and children be A and C, respectively Then we have the following system: .25C = 56.5 ----- Subtracting eq (ii) from eq (i) Number of children, or A + 226 = 429 ------ Substituting 226 for C in eq (i) Number of adults, or

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Tutor @MathTherapy has provided a clear solution using formal algebra.

Note that the answer can be obtained informally, USING EXACTLY THE SAME CALCULATIONS, without formal algebra:

If all 429 tickets had been adult tickets, the total cost would have been $429.

The actual total cost was $372.50, which is $56.50 less than $429.

The total cost decreases by $0.25 for each ticket that is a children's ticket instead of an adult ticket.

So the number of children's tickets was
56.50 56.50*4 226 ----- = ------- = --- = 226 0.25 0.25*4 1

ANSWER: 226 children's tickets, so 429-226 = 203 adult tickets

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