Chapter 8, Problem 25CR

To determine

An equation and the regular price of each box of cereal

Answer to Problem 25CR

The equation is $4\left(x-1.15\right)=8.40$

The regular price of each box of cereal is $x=3.25$ .

Explanation of Solution

Given:

Talia buys 4 boxes of cereal. She has coupons for $1.15 off the regular price of each box of cereal. After using the coupons, the total cost of the cereal is $8.40

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 box of cereal and $x-1.15$ is the discounted price of a box of cereal

4 times the discounted price of each box of cereal is $4\left(x-1.15\right)$

Thus, the equation is $4\left(x-1.15\right)=8.40$

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,

  $\begin{array}{c}4\left(x-1.15\right)=8.40\\ 4\cdot x+4\cdot \left(-1.15\right)=8.40\\ 4x-4.6=8.40\\ 4x-4.6+4.6=8.40+4.6\\ 4x=13\\ \frac{4x}{4}=\frac{13}{4}\\ x=3.25\end{array}$

Thus, the regular price of each box of cereal is $x=3.25$ .