Question

Write and solve a system of equations to figure it out

Answer 1

Solution:

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

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

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