Algebra One Word Problem

Question

At a local fitness center, members pay a $10 membership fee and $3 for each aerobics class. Nonmembers pay $5 for each class but no membership fee. For what number of aerobics classes will the cost of members and nonmembers be the same?

Answer 1

Hi Sara, 

To solve this problem, we can create a chart:

Step One: Where x equals the number of aerobics classes,

                            Members                   Nonmembers     

Cost in Dollars        10+3x                         0+5x             

Step Two: We create an equation to solve for x.

Member Cost=Nonmember Cost

10+3x= 0+5x

Step Three: Solve for x:

10+3x= 5x Subtract 3 from both sides

10=5x-3x Combine like terms

10=2x 

5=x

∴For five aerobics classes, the cost of members and nonmembers will be the same.

 

Answer 2

Hi Sara, let x represent the number of aerobics classes taken. We can set up an equation to represent the information given:

 

Equation:

 

10 + 3x = 5x

 

10 + 3x is the cost for the members

 

5x is the cost for nonmembers and must equal the cost for the members.

 

Solve the equation:

 

10 + 3x = 5x

 

Subtract 3x from both sides of the equation.

 

2x = 10

 

Divide both sides by 2:

 

x = 5

 

If both the members and nonmembers take 5 aerobics classes, they will have paid the same amount of money.

 

Check:

 

Substitute for x in the equation:

 

10 + 3 * 5 = 5 * 5

 

25 = 25, values check.

 

Questions?