Question

A movie theater sells adult tickets for $6 each. Senior citizens receive a discount of $3. One evening the theater sold 400 tickets and took in $2070 in revenue. How many tickets were sold to senior citizens?

Answer 1

Number of senior citizen tickets sold= 110

Number of adults tickets sold= 290

Explanation:

First, we need to establish a system of equations:

x= number of adults tickets

y= number of senior citizen tickets

x + y= 400

6x + 3y= 2,070

Now, we isolate x in one equation and substitute the value in the other:

x= 400 - y

6*(400 - y) + 3y = 2,070

2,400 - 6y + 3y = 2,070

330 = 3y

110 = y

Number of senior citizen tickets sold= 110

Number of adults tickets sold= 290

Prove:

290 + 110= 400

6*290 + 3*110= 2,070