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Mr. Ramirez purchased 50 concert tickets for a total of $575. The concert tickets cost $15 for adults and $10 for children under the age of 12.

Write and solve a system of equations to represent the given scenario. Use the variables "a" for adults and "c" for children.

Respuesta :

Answer: He purchased 15 adult tickets and 35 child tickets.

Explanation:
a = adult tickets
c = child tickets

a + c = 50
15a + 10c = 575

The first equation can be rearranged and substituted into the second equation.

a = 50 - c
15(50 - c) + 10c = 575
750 - 15c + 10c = 575
750 - 5c = 575
-5c = -175
c = 35

The value of c can be substituted into either one of the original equations to find a.

a + c = 50
a + 35 = 50
a = 15

Check:
a + c = 50
15 + 35 = 50
50 = 50

15a + 10c = 575
15*15 + 10*35 = 575
225 + 350 = 575
575 = 575

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