an adult ticket to a school play cost $5 a student ticket cost $3. $460 was collected of 120 tickets How many student tickets were sold how many adult tickets w

Question

algebra 1  

Answer 1

Hi Rosie,

 

Let number of Adult tickets sold  be x

     number of student tickets sold be y

 

Adult ticket costs $ 5, student ticket costs $ 3, Total collected $460,

 

5x+3y= 460......eq 1

 

Total number of tickets sold = 120 so

x+y=120, Multiply eq by 3, we get 3x+3y=360, subtract it from eq 1

 

5x+3y=460

-3x-3y=-360

we get,

2x = 100

x=50

x+y = 120, x= 50 so y=70

No of Adult tickets sold = 50, No of Student tickets sold = 70

 

 

 

 

Answer 2

We will represent adults as x and students as y. Each adult ticket was $5 and each student ticket was $3, so we can write the equation as

 

5x + 3y = 460

 

We also know that the total number of tickets sold between the students and adults was 120. A second equation we make because of that is 

 

x + y = 120

 

Now we have to ways to represent x and y and we need to use one to solve the other. I am going to rearrange the second equation to get y by itself. 

 

y = 120 - x

 

Now we plug this equation in for y in the top equation so 5x + 3y = 460 becomes

 

5x + 3(120 - x) = 460  then we distribute

 

5x + 360 - 3x = 460

 

 

combine like factors

 

2x + 360 = 460

 

2x =100

x = 50

 

So we sold 50 adult tickets (x) and since there were 120 tickets sold total we know that we sold 70 student tickets

 

Then we double check our math. 50 adult tickets x $5 each is $250  

70 student tickets x $3 each = $210

 

$210 + $250 = $460

 

Answer: 50 adult tickets and 70 student tickets