Question 235609: Adult tickets to a show are $9. Student tickets are $6. If you sold 29 tickets for a total of $210, how many adult tickets did you sell
only use 1 variable
Answer by MathPro(14)   (Show Source):
You can put this solution on YOUR website! Good Afternoon,
Your problem is:
Adult tickets to a show are $9. Student tickets are $6. If you sold 29 tickets for a total of $210, how many adult tickets did you sell
only use 1 variable
We are given that the total amount of tickets sold is 29. In words this means that the number of adult tickets + the number of student tickets = 29
I’ll digress for a moment and ask you to imagine if the total number of tickets was 3 and we were told that the number of adult tickets sold was 1 , then that would mean the number of student tickets sold would be 3 – 1 = 2.
Let’s apply this to our problem. Call the number of adult tickets sold, x, then the number of student tickets sold is 29 – x.
I’ll just digress and say that if you bought two items at 50 cents each the total cost would be 2($0.50) = $1.00
We are told that adult tickets are $9.00 each, so the total cost of all the adult tickets together is $9(x) and similarly the total cost of the student tickets is $6(29 – x). We are given that the total price of the adult and student tickets combined is $210.00. We can write this as:
$9x + $6(29 – x) = $210 equation (1)
Multiply out the second term:
$9x + $6(29) - $6x = $210
$3x + $174 = $210
Subtract $174 from both sides
$3x = $210 - $174 = $36
Divide both sides by $3:
$3x/$3 = $36/$3
In the same way that 3/3 = 1, $/$ = 1. So we get
x = 12
This means 12 adult tickets was sold and (29 -12) = 17 student tickets was sold
Let’s check the answer by substituting for x into equation (1)
$9(12) + $6(17) = $210
The left side is equal to the right side so our answer is correct.
Good Luck!
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