need help please

Question

​There were 1245 people who attended the school play last weekend. Student tickets cost $5 each and adult tickets cost $8 each. If they collected $7491 in total ticket sales, how many of each type of ticket was sold?

Answer 1

Hello Ty,

Let's write an equation using made up variable and the values give in the word problem. Let's define the variable:

s = the number of students who attend the school play

a = the number of adults who attend the school play

Now,

s + a = 1245

To find the total amount of revenue collected from ticket sales, multiply the number of students in attendance times their ticket price per student and likewise for the adults:

5s + 8a = 7491

So, we have to equation and two unknown variables. Whenever you have the same number of equations as the number of variable, the values of all variable can be found. In this case, lets rearrange the first equation and then plug it into the second equation:

s = 1245 - a

5(1245 - a) + 8a = 7491

Simplify and then solve for a:

6225 - 5a + 8a = 7491

3a = 1266

a = 422 students in attendance

Finally, plug this value of "a" into the first equation and solve:

s + 422 = 1245

s = 823 adults in attendance