Question

Write and solve a system of equations to figure it out

Answer 1

Let the number of youths tickets be

`=x`

Let the number of adult tickets be

`=y`

The price of each youth ticket is

`=\text{ \$5}`

The price of each adult ticket is

`=\text{ \$8}`

The total amount collected after sales is

`=\text{ \$377}`

The total number of tickets sold is

`=61`

Step 1:

write out the equation to show the amount of money collected

`5x+8y=377\ldots\ldots\ldots\ldots(1)`

Step 2:

Write out the equation to show the number of tickets sold

`x+y=61\ldots\ldots\ldots\ldots\text{.}(2)`

Step 3:

Solve the equations simultaneously

From equation (2) make x the subject of the formula to make equation 3

`\begin{gathered} x+y=61 \\ x=61-y\ldots\text{.}\ldots\ldots(3) \end{gathered}`

Step 4:

Substitute equation (3) in equation (1) in substitution method

`\begin{gathered} 5x+8y=377 \\ 5(61-y)+8y=377 \\ 305-5y+8y=377 \\ 305+3y=377 \\ \text{substract 305 from both sides} \\ 305-305+3y=377-305 \\ 3y=72 \\ \text{divide both sides by 3} \\ (3y)/(3)=(72)/(3) \\ y=24 \end{gathered}`

Step 5:

Substitute y=24 in the equation (3)

`\begin{gathered} x=61-y \\ x=61-24 \\ x=37 \end{gathered}`

Hence,

The number of youth tickets sold = x = 37

The number of adults tickets sold = y = 24