A local community theater group sells tickets for their upcoming play. A student ticket co… — ACT

A local community theater group sells tickets for their upcoming play. A student ticket costs $8$ dollars, which is $4$ dollars less than half the price of an adult ticket. If $a$ represents the cost of an adult ticket in dollars, what is the value of $a$ ?

A
$6$
B
$8$
C
$12$
D
$20$
$24$ Answer

Answer

The cost of the adult ticket is

24

dollars.

The correct answer is

24

. According to the problem, the student ticket price of

8

dollars is equal to

4

dollars less than half the price of the adult ticket (

a

). This relationship can be expressed algebraically as

8 = \frac{1}{2}a - 4

. Adding

4

to both sides of the equation results in

12 = \frac{1}{2}a

. Multiplying both sides by

2

yields

a = 24

Step-by-Step Solution

Translate the word problem into a linear equation.

8 = \frac{1}{2}a - 4

The student ticket price (

8

dollars) is equal to

4

dollars subtracted from half the price of the adult ticket (

a

Isolate the variable term by adding

4

to both sides of the equation.

12 = \frac{1}{2}a

To solve for

a

, we first eliminate the constant subtraction on the variable's side.

Solve for

a

by multiplying both sides of the equation by

2

a = 24

Multiplying by the reciprocal of

\frac{1}{2}

isolates the variable

a

Key Concept

Translating verbal statements into two-step linear equations and solving for the unknown variable.

Question

Answer

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Key Concept

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