Question

A GROUP OF 11 PEPLE ARE GOING TO THE MOVIES ONE SATURDAY. ADULT TICKETS COST $11.50 EACH AND CHILD TICKETS COST $7.25 EACH. IF THE TOTAL COST FOR ADMISSION TO THE MOVIE IS 105.25, HOW MUCH CHILDREN ATTENDED THE MOVIE?

Answer 1

5 children tickets
and 6 adult tickets

Answer 2

Let A and C be the number of adults and children respectively.
From the problem statement:\[\left\{A+C=11,\frac{115}{10}A+\frac{725}{100}C=\frac{10525}{100}\right\}\]The decimal numbers have been converted to integer fractions.
Why would one do that? In the general case, integer fractions guarantee an exact symbolic answer.

Solve the equations for C.