The manager of a movie theater found that Saturdays sales were $3675. He knew that a total of 650 tickets were sold on saturday.
2 answers:
Answer
250 adult tickets were sold and 400 children tickets were sold
Step by Step Explanation:
Given
Saturday Sales: $3675
Total tickets: 650
Cost of adult tickets = $7.50
Cost of children tickets = $4.50
Let A represent the adult tickets and C represent the children tickets,
if there's a total of 650 tickets, then
A + C = 650
Also,
if an adult ticket cost $7.50 and a child ticket cost $4.50 then
7.5A + 4.5C = 3675
From these, we have a simultaneous equation
A + C = 650 ------- (1)
7.5A + 4.5C = 3675 ----------(2)
Make A the subject of formula in (1)
A + C = 650 becomes
A = 650 - C
Substitute 650 - C for A in (2), we have
7.5(650 - C) + 4.5C = 3675
Open the bracket
4875 - 7.5C + 4.5C = 3675
4875 - 3C = 3675
Collect like terms
-3C = 3675 - 4875
-3C = -1200
Divide through by -3
C = 400
Recall that
A = 650 - C
So, A = 650 - 400
A = 250
Hence, 250 adult tickets were sold and 400 children tickets were sold
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