Question

The Lehman band raised $1,670 by selling tickets to their winter concert. They sold student tickets $4 each and adult tickets for $9 each. A total of 300 student and adult tickets were sold. Write a system of equations could be solve for the number of student and adult tickets sold at the concert.

Answer 1

`\left\{\begin{matrix}x + y = 300\qquad\qquad [1]\\ 9y + 4x = 1,670\qquad\qquad [2]\end{matrix}\right.`

Explanation:

System of Equations

Let's call:

x=Number of student tickets

y=Number of adult tickets

Conditions:

A total of 300 people bought tickets. The equation to model this condition is:

`x + y = 300\qquad\qquad [1]`

Each adult ticket costs $9. If y adults paid for the concert, then 9y dollars of the total come from adults.

Each student ticket costs $4. If x students paid for the concert, then 4x dollars of the total come from students.

The total raised by The Lehman band was $1,670, thus:

`9y + 4x = 1,670\qquad\qquad [2]`

The system of equations is:

`\left\{\begin{matrix}x + y = 300\qquad\qquad [1]\\ 9y + 4x = 1,670\qquad\qquad [2]\end{matrix}\right.`