The school production of? 'Our Town' was a big success. For opening? night, 410 tickets were sold

Question

The school production of? 'Our Town' was a big success. For opening? night, 410 tickets were sold. Students paid ?$2.50 ?each, while? non-students paid ?$4.50each. If a total of $ 1251.00 was? collected, how many students and how many? non-students attended?

Answer 1

This is a multi-step problem. First we need to determine two different equations to represent the two values we need to know. Equation 1 represents the number of tickets sold. Equation 2 represents the total amount of money raised.

 

The sum of the number of students and non-students is equal to 410. 

If x=number of students and y=number of non-students then x+y=410

 

The total amount of money raised was $1251. 

2.5x=money from student tickets and 4.5y=money from non-student tickets

Our equation would look like this: 2.5x+4.5y=1251

 

In order to solve the second equation, we have to solve the first equation for either x or y. (solve for x)

x+y=410 (subtract x from both sides)

x=410-y

 

We then replace x in the second equation with the x in terms of y 

2.5x+4.5y=1251 (solve for y)

2.5(410-y) +4.5y=1251

1025-2.5y+4.5y=1251 (combine the y's)

1025-2y=1251 (subtract 1025 from both sides)

-2y=226 (divide by -2)

y=-113 (multiply by -1)

y=113 

 

Now we can replace y in the first equation with our value for y: 113

x+y=410

x+113=410

x=297 

 

We can check our work by plugging these values into each equation.

x+y=410

297+113=410

410=410

 

2.5x+4.5y=1251

2.5(297)+4.5(113)=1251

742.5+508.5=1251

1251=1251

 

So, because our work checks out and the equations are true, we know that 297 students and 113 non-students  attended. 

 

Hope this helps!