A concert manager counted 600 ticket receipts the day after a concert. The price for a student ticket was $13.50, and the price for an adult ticket was $15.00. The register confirms that $8,587.50 was taken in. How many student tickets and adult tickets were sold?

165 student tickets and 435 adult tickets were sold

Step-by-step explanation:

In this question, we are asked to calculate the number of students and adults tickets sold.

since we do not know these numbers, let the number of student tickets sold be s and the number of adult tickets sold be a

From the question, we are told that a total of 600 tickets were sold.

mathematically, this means that;

a + s = 600 •(i)

The price of students ticket sold is $13.5, this means the total money realized from sales of student ticket = $13.5s

The price of adult ticket sold is $15, this means the total money realized from the sales of adult ticket is $15a

Adding both yields a total of $8,587.5

Hence, mathematically;

13.5s + 15a = 8,587.5. ••••••••(ii)

From equation 1, a = 600 - s , we can input this in the second equation to yield;

13.5s + 15(600-s) = 8,587.5

13.5s + 9,000 - 15s = 8,587.5

2.5s = 9,000 - 8587.5

2.5s = 412.5

s = 412.5/2.5

s = 165 student tickets

Number of adult tickets = 600 - s = 600 - 165 = 435

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

48 / 6 = x

in this case, x will equal the amount of money in each card!

x therefore will be 8.

trent had $8 in each birthday card.