Chapter 8.4, Problem 28IP

To determine

What is the regular price of admission.

Answer to Problem 28IP

  $\$12.50$

Explanation of Solution

Given:

The passes are good for $2.95 off the regular price of admission , total 5 friends going to the theater and spend $47.75 total on admission.

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 the regular price of admission, let a be the regular price of admission, first subtracting the good passes off for the regular price that is $2.95 from the regular price, then multiplying it by 5 number of friends going to the theater is equal to $47.75 the total they spend then the equation is as shown below:

  $5(a-2.95)=47.75$

Now, to solving the equation first using distributive property on left side of the equation and then isolate the variable term a on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate a on left side, first add 14.75 both sides and then divide both sides by 5 and then simplify further as shown below,

  $\begin{array}{l}5(a-2.95)=47.75\\ 5\cdot a-5\cdot 2.95=47.75\\ 5a-14.75=47.75\\ 5a-14.75+14.75=47.75+14.75\\ 5a=62.5\\ \frac{5a}{5}=\frac{62.5}{5}\\ a=12.5\end{array}$

So, the regular price of admission is $12.50 .