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Guillermo bought textbooks and notebooks at the bookstore. The number of textbooks was $3$ more than the number of notebooks. He bought $5$ textbooks. How many notebooks did he buy?
2
Gerry worked Sudoku puzzles and crossword puzzles this week. The number of Sudoku puzzles he completed is seven more than the number of crossword puzzles. He completed $14$ Sudoku puzzles. How many crossword puzzles did he complete?
7
In Solve Sales Tax, Commission, and Discount Applications , we learned how to translate and solve basic percent equations and used them to solve sales tax and commission applications. In the next example, we will apply our Problem Solving Strategy to more applications of percent.
Nga's car insurance premium increased by $\text{\$60},$ which was $\text{8\%}$ of the original cost. What was the original cost of the premium?
Step 1. Read the problem. Remember, if there are words you don't understand, look them up.  
Step 2. Identify what you are looking for.  the original cost of the premium 
Step 3. Name. Choose a variable to represent the original cost of premium.  Let $c=\text{the original cost}$ 
Step 4. Translate. Restate as one sentence. Translate into an equation. 

Step 5. Solve the equation.  
Divide both sides by 0.08.  
Simplify.  $c=750$ 
Step 6.
Check: Is our answer reasonable? Yes, a $750 premium on auto insurance is reasonable. Now let's check our algebra. Is 8% of 750 equal to 60?


Step 7. Answer the question.  The original cost of Nga's premium was $750. 
Pilar's rent increased by $\text{4\%}.$ The increase was $\text{\$38}.$ What was the original amount of Pilar's rent?
$950
Steve saves $\text{12\%}$ of his paycheck each month. If he saved $\text{\$504}$ last month, how much was his paycheck?
$4,200
Now we will translate and solve number problems . In number problems, you are given some clues about one or more numbers, and you use these clues to build an equation. Number problems don't usually arise on an everyday basis, but they provide a good introduction to practicing the Problem Solving Strategy . Remember to look for clue words such as difference , of , and and .
The difference of a number and six is $13.$ Find the number.
Step 1. Read the problem. Do you understand all the words?  
Step 2. Identify what you are looking for.  the number 
Step 3. Name. Choose a variable to represent the number.  Let $n=\text{the number}$ 
Step 4.
Translate. Restate as one sentence.
Translate into an equation. 

Step 5.
Solve the equation.
Add 6 to both sides. Simplify. 

Step 6.
Check:
The difference of 19 and 6 is 13. It checks. 

Step 7. Answer the question.  The number is 19. 
The difference of a number and eight is $17.$ Find the number.
25
The difference of a number and eleven is $\mathrm{7}.$ Find the number.
4
The sum of twice a number and seven is $15.$ Find the number.
Step 1. Read the problem.  
Step 2. Identify what you are looking for.  the number 
Step 3. Name. Choose a variable to represent the number.  Let $n=\text{the number}$ 
Step 4.
Translate. Restate the problem as one sentence.
Translate into an equation. 

Step 5. Solve the equation.  
Subtract 7 from each side and simplify.  
Divide each side by 2 and simplify.  
Step 6.
Check: is the sum of twice 4 and 7 equal to 15?


Step 7. Answer the question.  The number is 4. 
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