Question

A local theater sold 135 tickets to a matinee play with a total revenue of $2,367.00where they charged $25.00 for an adult ticket and $13.00 for a child's ticket. Usingthe variables a and c to represent the number of adult tickets sold and the number ofchildren's tickets sold respectively, determine a system of equations that describes thesituation.Enter the equations below separated by a comma.How many adult tickets were sold?How many children's tickets were sold?Pls see the picture

Answer 1

Given:

• Total number of tickets sold = 135

,

• Total revenue = $2,367.00

,

• Cost of each adult ticket = $25.00

• Cost of each child ticket = $13.00

Let's write a system of equations that describes this situation.

Let a represent number of adults tickets sold.

Let c represent number of children tickets sold.

We have the system of equations:

• a + c = 135

,

• 25a + 13c = 2367

Let's solve the system using substitution method.

• Rewrite the first equation for a.

Subtract c from both sides:

a + c - c = 135 - c

a = 135 - c

• Substitute (135 - c) for a in equation 2:

25(135 - c) +13c = 2367

Apply distributive property:

25(135) + 25(-c) + 13c = 2367

3375 - 25c + 13c = 2367

3375 - 12c = 2367

• Subtract 375 from both sides:

3375 - 3375 - 12c = 2367 - 3375

-12c = -1008

Divide both sides by -12:

`\begin{gathered} (-12c)/(-12)=(-1008)/(-12) \\ \\ c=84 \end{gathered}`

Substitute 84 for c in any of the equations:

a = 135 - c

a = 135 - 84

a = 51

We have:

a = 51, c = 84

Therefore, 51 adult tickets and 84 children tickets were sold.

ANSWER:

• System of equations:

a + c = 135, 25a + 13c = 2367

• Number of adult tickets sold = 51

,

• Number of children tickets sold = 84