Chapter 8, Problem 26CR

To determine

An equation and the regular price of each box of cereal

Answer to Problem 26CR

The equation is $5\left(x-4\right)=55$

The regular price of each T-shirt is $x=15$ .

Explanation of Solution

Given:

Brady buys five T-shirt on sale for $4 off the regular price and total cost is $55 before tax

Concept Used:

Left distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$

• 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 price

Let x be the price of each T-shirt and $x-4$ is the discounted price of a T-shirt

5 T-shirt on sale, so the discounted price of each box of cereal is $5\left(x-4\right)$

Thus, the equation is $5\left(x-4\right)=55$

Here to isolate x on left side, first use the Left distributive property and then add both sides by $4.6$ and then divide both sides by $4$ and then simplify further as shown below,

  $\begin{array}{c}5\left(x-4\right)=55\\ 5\cdot x+5\cdot \left(-4\right)=55\\ 5x-20=55\\ 5x-20+20=55+20\\ 5x=75\\ \frac{5x}{5}=\frac{75}{5}\\ x=15\end{array}$

Thus, the regular price of each T-shirt is $x=15$ .