How does one show his work for this question?

Question

240 tickets were pre sold. Children’s and adult tickets were sold at a ratio of 7:1.

How many children’s tickets were sold?

How many adult tickets were sold?

Answer 1

Let A = #of adult tickets sold

C = #of children tickets sold.

With two unknowns two equations are required.

First equation is sort of obvious.

A + C = 240

If the ration of children's tickets to adult tickets is 7 to 1, we can write:

C/A = 7/1 or C = 7A

Now substitute the fact that C = 7A into the first equation (replacing C with 7A).

A + 7A = 240

8A = 240

A = 240/8 = 30 (#adult tickets)

C = 7(30) = 210 (#childrren tickets)

Note that 210:30 as 7:1 and 210 + 30 = 240.