Question

A small movie theater sells children's tickets for $4 each and adult tickets for $10 each for an animated movie. The theater sells a total of $338 in ticket sales.

(c) show that after multiplying both sides of the equation in (a) by 2, c=52 and a=18 is still a solution to this equation.

Equation: 4c+10a=388

Answer 1

Let c = number of children's tickets sold

Let a = number of adults tickets sold

Given:

• Cost of child ticket = $4
• Cost of adult ticket = $10
• Total ticket sales = $388

⇒ 4c + 10a = 388

Multiply both sides of the equation by 2:

⇒ 2(4c + 10a) = 2 × 388

⇒ 8c + 20a = 776

If c = 52 and a = 18, substitute these values into the equation and solve:

⇒ 8(52) + 20(18)

⇒ 416 + 260

⇒ 776

As 776 = 776, this proves that c = 52 and a = 18 is a solution to this equation.

Answer 2

Proved below!

Explanation:

Start by multiplying both sides by 2 (as said in the question):

`\implies 4c + 10a = 388`

`\implies 2(4c + 10a) = 2(388)`

`\implies 8c + 20a = 776`

Substitute the solution(s) in the equation:

`\implies 8(52) + 20(18) = 776` (c = 52; a = 18)

`\implies 416 + 360 = 776`

`\implies \bold{776 = 776 \ \ \ (Proved)}`