Exercise 92 Page 85

We are asked to define a variable and write an equation for the given problem. We will then solve the equation and write our solution as a sentence. Let's write down the most important information from the problem.

• A student ticket costs $3.
• An adult ticket costs $5.
• A total of $4730 was collected.
• The number of students attending the play was 150 more than the number of adults attending.

Let's define the variable x as the number of students who attended the play. The number of adults who attended is 150 less than the number of students attending, so the number of adults at the play was x - 150. Number of Students:& x Number of Adults:& x - 150 The cost of a student ticket was $3, so the total collected from the sale of student tickets was 3x. Since the cost of an adult ticket was $5, the total collected from the sale of adult tickets was 5(x- 150). Remember, the total amount of money collected was $4730. This lets us write an equation. 3x + 5(x- 150) = 4730 Now we can solve the equation. To do so, we will isolate x on the left-hand side and simplify.

3x + 5(x-150) = 4730

▼

Solve for x

Distr

Distribute 5

3x + 5x - 5*150 = 4730

AddTerms

Add terms

8x - 5*150 = 4730

Multiply

Multiply

8x - 750 = 4730

AddEqn

LHS+750=RHS+750

8x - 750 + 750 = 4730 + 750

AddTerms

Add terms

8x = 5480

DivEqn

.LHS /8.=.RHS /8.

8x/8 = 5480/8

CalcQuot

Calculate quotient

x = 685

The number of students who attended the play was 685.