Please somebody explain how to solve word problem

Question

At the city museum, child admission is 5.90 and adult admission is 9.10. On Wednesday, 3 times as many adult tickets as child tickets were sold for a total sale of 962.80. How many child tickets were sold that day?

Answer 1

Ok the first step is to define variables:

x = children

y = adult

next you can write equations from the facts that you are given:

5.9x + 9.1y = 962.8

y = 3x

now you can use either substitution or elimination to solve. I recommend substitution.

5.9x + 9.1(3x) = 962.8

5.9x + 27.3x = 962.8

33.2x = 962.8

x = 29 --> 29 children's tickets

y = 3(29)

y = 87 --> 87 adult tickets

Answer 2

Hi Anissa, thanks for asking!

In this problem we’ll let C = number of child tickets and A = number of adult tickets.

We’re told that the number of adult tickets is larger than the number of child tickets (3 times as large). That means that A = 3C. Since we’re told the prices of child and adult tickets, we also know that 5.90C + 9.10A = 962.80.

If we replace A with 3C into the second equation, then we have 5.90C + 9.10*(3C) = 962.80.

That means when we simplify the left hand side: 27.30C = 962.80, or C = 29 child tickets.

Using this answer back in the first equation, we then have A = 3(29) = 87 adult tickets.

Please let me know if I can be more helpful!

Joe