Chapter 8.2, Problem 51IP

To determine

The number of months the family can use the club

Answer to Problem 51IP

The number of months the family can use the club is $f=15$ .

Explanation of Solution

Given:

The cost of a family membership at a health club is shown below.

  

The Johnson family budgets $800 to use the health club and the equation, $125+45f=800$

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $125+45f=800$ for the variable, isolate the variable term f on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate f on left side, first subtract both sides by $125$ and then divide both sides by $45$ and then simplify further as shown below,

  $\begin{array}{c}125+45f=800\\ 125+45f-125=800-125\\ 45f=675\\ \frac{45f}{45}=\frac{675}{45}\\ f=15\end{array}$

Thus, the number of months the family can use the club is $f=15$ .