8.1 Solve equations using the subtraction and addition properties  (Page 4/6)

Shayla paid $\text{\$24,575}$ for her new car. This was $\text{\$875}$ less than the sticker price. What was the sticker price of the car?

Solution

What are you asked to find?	"What was the sticker price of the car?"
Assign a variable.	Let $s=$ the sticker price of the car.
Write a sentence that gives the information to find it.	$24,575 is $875 less than the sticker price $24,575 is $875 less than $s$
Translate into an equation.
Solve.
Check:
Is $875 less than $25,450 equal to $24,575?
$\mathrm{25,450}-875\stackrel{?}{=}\mathrm{24,575}$
$\mathrm{24,575}=\mathrm{24,575}✓$
Write a sentence that answers the question.	The sticker price was $25,450.

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Key concepts

• Determine whether a number is a solution to an equation.
  1. Substitute the number for the variable in the equation.
  2. Simplify the expressions on both sides of the equation.
  3. Determine whether the resulting equation is true.
  If it is true, the number is a solution.
  If it is not true, the number is not a solution.
• Subtraction and Addition Properties of Equality
  • Subtraction Property of Equality
    For all real numbers a, b, and c ,
    if a = b then $a-c=b-c$ .
  • Addition Property of Equality
    For all real numbers a, b, and c ,
    if a = b then $a+c=b+c$ .
• Translate a word sentence to an algebraic equation.
  1. Locate the “equals” word(s). Translate to an equal sign.
  2. Translate the words to the left of the “equals” word(s) into an algebraic expression.
  3. Translate the words to the right of the “equals” word(s) into an algebraic expression.
• Problem-solving strategy
  1. Read the problem. Make sure you understand all the words and ideas.
  2. Identify what you are looking for.
  3. Name what you are looking for. Choose a variable to represent that quantity.
  4. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebra equation.
  5. Solve the equation using good algebra techniques.
  6. Check the answer in the problem and make sure it makes sense.
  7. Answer the question with a complete sentence.