Question

A science museum charges an admission fee of $10 per adult and $6 per child. If the museum had 2,000 visitors on a particular day and the total collection was $18,800, how many adults and children visited the museum?

Answer 1

a = adult
c = child

10a + 6c = 18,800
a + c = 2,000

In the second equation, subtract c from both sides.

a = 2000 - c

Put this into the first equation.

10(2000 - c) + 6c = 18800

Multiply everything in the parenthesis by 10.

20,000 - 10c + 6c = 18,800

Combine like terms.

20,000 - 4c = 18,800

Subtract 20,000 from both sides.

-4c = -1,200

Divide -4 on both sides.

c = 300

Put this into the second equation.

a + 300  = 2,000

Subtract 300 from both sides.

a = 1,700

Hope this helps!