Solve Equations Using the Subtraction and Addition Properties of Equality: example 2.12

Randell paid $28,675 for his new car. This was $875 less than the sticker price. What was the sticker price of the car?

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Translate into an algebraic equation and solve:

Eddie paid $19,875 for his new car. This was $1,025 less than the sticker price. What was the sticker price of the car?

How did it go?

Step 1. Read the problem.
Step 2. Identify what we are looking for.	"What was the sticker price of the car?"
Step 3. Name what we are looking for. Choose a variable to represent that quantity.	Let $s =$ the sticker price of the car.
Step 4. Translate into an equation. Restate the problem in one sentence.	$28,675 is $875 less than the sticker price
Step 5. Solve the equation.	$$28,675 is $875 less than s$ $\begin{matrix} \begin{matrix} 28,675 & = & s - 875 \\ 28,675 + 875 & = & s - 875 + 875 \\ 29,550 & = & s \end{matrix} \end{matrix}$
Step 6. Check the answer. Is $875 less than $29,550 equal to $28,675? $\begin{matrix} \begin{matrix} 29,550 - 875 & \overset{?}{=} & 28,675 \\ 28,675 & = & 28,675 ✓ \end{matrix} \end{matrix}$
Step 7. Answer the question with a complete sentence.	The sticker price of the car was $29,550.

Step 1. Read the problem.
Step 2. Identify what we are looking for.	"What was the sticker price of the car?"
Step 3. Name what we are looking for. Choose a variable to represent that quantity.	Let $s =$ the sticker price of the car.
Step 4. Translate into an equation. Restate the problem in one sentence.	$28,675 is $875 less than the sticker price
Step 5. Solve the equation.	$$28,675 is $875 less than s$ $\begin{matrix} \begin{matrix} 28,675 & = & s - 875 \\ 28,675 + 875 & = & s - 875 + 875 \\ 29,550 & = & s \end{matrix} \end{matrix}$
Step 6. Check the answer. Is $875 less than $29,550 equal to $28,675? $\begin{matrix} \begin{matrix} 29,550 - 875 & \overset{?}{=} & 28,675 \\ 28,675 & = & 28,675 ✓ \end{matrix} \end{matrix}$
Step 7. Answer the question with a complete sentence.	The sticker price of the car was $29,550.