Chapter 8.4, Problem 13GP

To determine

What is the ice skating rink’s entrance fee.

Answer to Problem 13GP

  $\$5$

Explanation of Solution

Given:

Mr vargas takes his class of 24 students ice skating . Each students pay an entrance fee for skates is $4 and the total cost of both rinks and skates is $216.

Concept Used:

Distributive property:

Left Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$

Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$

• 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 find the ice skating rink’s entrance fee, let f be the rink’s entrance fee and $4 is the skates entrance fee as given, now adding both the entrance fee and then multiplying it by 24 because total students are 24 , then the equation is equal to 216 total cost , now the equation is as shown below:

  $24\left(f+4\right)=216$

Now, to solving the equation first using distributive property on left side of the equation and then 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 96 from both sides and then divide both sides by 24 and then simplify further as shown below,

  $\begin{array}{l}24\left(f+4\right)=216\\ 24\cdot f+24\cdot 4=216\\ 24f+96=216\\ 24f+96-96=216-96\\ 24f=120\\ \frac{24f}{24}=\frac{120}{24}\\ f=5\end{array}$

So, the cost of rink’s entrance fee is $\$5$ .