Question

Tickets to the local carnival cost $5.50 for adults and $3.00 for children under the age of 12. A group of 8 people bought tickets to the carnival for $36.50. Write a system of equations to represent this scenario. How many adult tickets were sold?

Answer 1

The number of adult tickets sold was 5

Explanation:

Let

x ----> the number of adult tickets

y ----> the number of child tickets

we know that

`x+y=8`

isolate the variable y

`y=8-x` ----> equation A

`5.50x+3y=36.50` ----> equation B

Solve the system by substitution

substitute equation A in equation B

`5.50x+3(8-x)=36.50`

solve for x

apply distributive property left side

`5.50x+24-3x=36.50`

combine like terms

`2.50x+24=36.50`

subtract 24 both sides

`2.50x=36.50-24`

`2.50x=12.50`

Divide by 2.50 both sides

`x=5`

therefore

The number of adult tickets sold was 5