An amusement park sells child and adult tickets at a ratio of 8:1. On Saturday, they sold 147 more child tickets that adult tickets. How many tickets did the amusement park sell on Saturday?

Answer 1

Altogether they sold N tickets

X + x+147 = N where x is the # of adult tickets

2x + 147 = N <--- please label this equation ALPHA; we need it later!

Because the ratio is 8 to 1,

x = N/9 is the number of adult tickets

and

x+147 = (8/9) N is the number of child tickets

Because there are 2 unknowns ( N and x) we need 2 equations, but have 3!!!

First, since x = N/9 ----> 9x = N

substituting this into equation ALPHA above in bold:

2x + 147 = 9x

147 = 7x <--- subtracts 2x from both sides

x = 21 <--- divides both sides by 7.

so there are 21 adult tickets,

21+147 = 168 child tickets for a total of

21+168 = 189 tickets.

Notice that 21/189 = 1/9 and 168/189 = 8/9

which is the 8 to 1 ratio.

189 tickets

Answer 2

The problem states that they are sold in a ratio of 8:1

This is the same as saying that 8/9 of the tickets are child's tickets, and 1/9 are adult tickets.

It then tells us that 8/9 (the number of child tickets sold) is 147 greater than 1/9 (the number of adult tickets sold).

We will use x for the total number of tickets sold, and then the problem looks like this:

(8/9)*x - (1/9)*x = 147

Or simplified:

(7/9)*x = 147

Then we solve for x:

(7/9)*(9/7)*x = 147*(9/7)

1*x = (147*9)/7

x = 1,323/7

x = 189

So the total tickets sold was 189. This means that we could ALSO figure out how many adult tickets were sold (even though the problem doesn't ask us to), by multiplying to total by 1/9 or dividing by 9 (these are mathematically the same thing).

From this, we know that the number of adult tickets sold was 21, and the number of child tickets sold was 168. If we take 168 (the child tickets sold) and divide by 21 (the adult tickets sold), we should get our original ratio: 8:1.

And if we subtract 21 from 168, we should get the difference that was given in the problem: 147.