At the city museum, child admission is $5.20 and adult admission is $9.30. On Thursday, 149 tickets were sold for a total sales of $1176.60. How many adult tickets were sold that day?

The Answer is: There are 51 child tickets and 98 adult tickets.

Step-by-step explanation:

Let c = the number of child tickets and a = the number of adult tickets. Adding these tickets up is equal to 149 total tickets.

a + c = 149.

Solve for a:

a = 149 - c

The number of child tickets times 5.20 plus the number of adult tickets times 9.30 is equal to $1,176.60. Equation below:

5.20c + 9.30a = 1176.60

5.20c + 9.30 (149-c) = 1176.60

5.20c + 1385.7 - 9.30c = 1176.60

-4.1c = 1176.60 - 1385.7

-4.1c = - 209.1

c = - 209.1 / - 4.1 = 51 child tickets.

Solve for a:

a = 149 - c

a = 149 - 51 = 98 adult tickets.

Proofs:

a + c = 149

98 + 51 = 149

And:

5.20c + 9.30a = 1176.60

5.20 (51) + 9.30 (98) = 1176.60

265.20 + 911.40 = 1176.60

1176.60 = 1176.60