SOLUTION: there are 429 people at a play. admission was $1.50 for adults and $0.75 for children the receipts totaled $371.25. How many adults and how many children attended the play?

Question 1203460: there are 429 people at a play. admission was $1.50 for adults and $0.75 for children the receipts totaled $371.25. How many adults and how many children attended the play?
Found 3 solutions by math_tutor2020, ikleyn, greenestamps:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

x = number of adults
429-x = number of children
1.50x = revenue from adults
0.75(429-x) = revenue from children
1.50x+0.75(429-x) = total revenue = 371.25

1.50x + 0.75(429-x) = 371.25
1.50x + 321.75 - 0.75x = 371.25
0.75x + 321.75 = 371.25
0.75x = 371.25 - 321.75
0.75x = 49.5
x = 49.5/0.75
x = 66 adults
429 - x = 429 - 66 = 363 children

Check:
66 adults + 363 children = 429 people total
66*1.50 + 363*0.75 = 371.25 dollars total
Both conditions are confirmed.

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Answers:
66 adults and 363 children

Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.
there are 429 people at a play.
admission was $1.50 for adults and $0.75 for children
the receipts totaled $371.25.
How many adults and how many children attended the play?
~~~~~~~~~~~~~~~~~

x adults; (429-x) children. Write the total money equation 1.50x + 0.75*(429-x) = 371.25. Simplify and find x 1.50x + 0.75*429 - 0.75x = 371.25 1.50x - 0.75x = 371.25 - 0.75*429 0.75x = 49.50 x = 49.50/0.75 = 66. ANSWER. 66 adults and 429-66 = 363 children. CHECK. 1.50*66 + 0.75*363 = 371.25 dollars, total money. ! correct !

Solved.

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

The solutions from the other tutors are good formal algebraic solutions.

If a formal algebraic solution is not required, here is an informal solution, using the fact that the cost of an adult ticket is exactly twice the cost of a child ticket.

Divide the total receipts by the cost of a child ticket:

The total receipts are enough to buy 495 child tickets.

But only 429 tickets were sold.

Since the cost of an adult ticket is twice the cost of a child ticket, the number of adults was 495-429 = 66.

ANSWER: 66 adults; 429-66 = 363 children

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