Question

The spring concert at a certain high school sold 150 tickets. Students were charged ​$3 each and adults ​$7 each. The income from the sale of tickets was ​$786. How many students and how many adults bought tickets?

Answer 1

66 student tickets and 84 adult tickets

Explanation:

Write a system of equations. When writing the equation, group together amounts that have the same labels. You can only use the amounts in one equation and not both. I am going to use x to represent student tickets and y to represent adult tickets.

`x + y = 150\\3x + 7y = 786`

I am going to use elimination to solve. To do this, I am going to eliminate the x variable first. I am going to multiply the first equation by -3. I am doing this so the x's have the exact same number, but one of them is negative and one is positive, so when they are added they will equal zero.

`-3(x+y = 150)\\-3x-3y=-450`

Your two new equations.

`-3x-3y=-450\\3x+7y=786`

Now add and solve for y.

`4y = 336\\4y/4=336/4\\y = 84`

Now solve for x. I am going to use the first equation and substitute 84 for y.

`x+y=150\\x+84=150\\x+84-84=150-84\\x=66`

Answer 2

• 66 student tickets
• 84 adult tickets

Explanation:

Let x represent the number of higher-value (adult) tickets. Then 150-x is the number of student tickets. The total income from sales was ...

7x +3(150-x) = 786

4x = 336 . . . . . . . . . simplify, subtract 450

x = 84 . . . . . . . . divide by 4; number of adult tickets sold

150-x = 66 . . . . number of student tickets sold

66 students and 84 adults bought tickets.