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The admission to a barrio entertainment was $0.50 for adults and $0.25 for children. The total receipts for 150 tickets amounted $62.50.
Find the number of adults and children admitted.
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Solution 1. System of two equations
a + c = 150, (1)
0.50a + 0.25c = 62.50. (2)
You can simplify it:
a + c = 150, (1')
50a + 25c = 6250. (2')
Express c = 150 - a from (1) and substitute into (2). You will get
50a + 25(150-a) = 6250 (3) (one equation for one unknown "a").
The rest is just arithmetic.
Solution 2. One equation
Let "a" be the number of adults.
Then the number of child admissions is 150-a.
The "value equation" is
50a + 25*(150-a) = 6250 (exactly as the equation (3) in the Solution 1 above.
The rest is just arithmetic.
