Chapter 8.2, Problem 77STP

To determine

The solution of the equation $3c-12=45$ to find the cost in dollars of the second pair of jeans

Answer to Problem 77STP

The solution of the given equation is $c=19$

Explanation of Solution

Given:

Jody bought two pairs of jeans and the first pair costs $12 less than 3 times the cost c of the second pair and the first pair of jeans costs $45 and the equation $3c-12=45$ for the second pair of jeans

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 $3c-12=45$ for the variable, isolate the variable term c on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate c on left side, first add both sides by $12$ and then divide both sides by $3$ and then simplify further as shown below,

  $\begin{array}{c}3c-12=45\\ 3c-12+12=45+12\\ 3c=57\\ \frac{3c}{3}=\frac{57}{3}\\ c=19\end{array}$

Thus, the solution of the given equation is $c=19$