Question

at a school concert the total value of tickets sold was $994. Student tickets sold for $5 and adult tickets sold for $8. The number of adults tickets sold was 14 more than 2 times the number of student tickets. How many student tickets and adult tickets were sold?

Answer 1

The total sold was 98 tickets for adults and 42 for students.

Explanation:

In order to calculate the number of tickets of each kind sold we need to create a system of equations with the given information. The first equation can be created is that the sum of adult tickets multiplied by its cost with the student tickets also multiplied by its cost must be equal to the total value of tickets sold, so:

`5*\text{students} + 8*\text{adults} = 994`

We also know that the number of adult tickets was 14 more than 2 times the number of student tickets, therefore:

`\text{adults} = 2*\text{students} + 14`

If we apply the second expression on the first one we can solve for the number of tickets sold to students, we have:

`5*\text{students} + 8*(2*\text{students} + 14)= 994\\5*\text{students} + 16*\text{students} + 112 = 994\\ 21*\text{students} = 994 - 112\\\text{students} = (882)/(21) = 42`

We can use this value to find the number of adults ticket sold:

`\text{adults} = 2*42 + 14\\\text{adults} = 98`

The total sold was 98 tickets for adults and 42 for students.

Answer 2

42 student tickets and 98 adult tickets

Explanation:

Let's call the number of student tickets 's' and the number of adult tickets 'a'.

Then, we can write the two equations below:

5s + 8a = 994

a = 2s + 14

Using the value of 'a' from the second equation in the first one, we have:

5s + 8*(2s + 14) = 994

5s + 16s + 112 = 994

21s = 882

s = 42

Now, finding the value of 'a', we have:

a = 2*42 + 14 = 98