1. 3
Solving Application Problems

2. R.1 Fractions
3.3 Solving Application Problems with One Unknown Quantity
Objectives
Translate word phrases into algebraic expressions.
Translate sentences into equations.
Solve application problems with one unknown quantity.

3. Translate word phrases into algebraic expressions.
Write each phrase as an algebraic expression. Use x as the variable.
Example
Words Algebraic Expression
A number plus 2
The sum of 8 and a number
5 more than a number
A number increased by 6
9 less than a number
A number subtracted from 3
A number decreased by 4
10 minus a number

4. Translate word phrases into algebraic expressions.
Write each phrase as an algebraic expression. Use x as the variable.
Example
Words Algebraic Expression
8 times a number
The product of 12 and a number
Double a number (meaning “2 times”)
The quotient of –6 and a number
A number divided by 10
15 subtracted from 4 times a number
The result is

5. Translate sentences into equations.
If 5 times a number is added to 11, the result is 26. Find the number.
Example
Let x represent the unknown number.
The number is 3.

6. Translate sentences into equations.
(continued)
Example
Check
We see that 5 • = = 26.

7. Solve application problems with one unknown quantity.

8. Solve application problems with one unknown quantity.
Example
Heather put some money aside in an envelope for small household expenses. Yesterday she took out $20 for groceries. Today a friend paid back a loan and Heather put the $34 in the envelope. Now she has $43 in the envelope. How much was in the envelope at the start?
Step 1
Read the problem:
Unknown: amount of money in the envelope at the start
Known: took out $20; put in $34; ended up with $43

9. Solve application problems with one unknown quantity.
Example
(continued)
Step 2(a)
Assign a variable: Let m represent the money at the start.
Step 3
Write an equation:

10. Solve application problems with one unknown quantity.
Example
(continued)
Step 4
Solve the equation:

11. Solve application problems with one unknown quantity.
(continued)
Example
Step 5
State the answer: There was $29 in the envelope.
Step 6
Check the answer:
Started with $29 in the envelope
Took out $20, so $29 – $20 = $9 in the envelope
Put in $34, so $9 + $34 = $43
Now has $43

12. Solve application problems with one unknown quantity.
Example
Michael has completed 5 less than three times as many lab experiments as David. If Michael has completed 13 experiments, how many experiments has David completed?
Step 1
Read the problem:
Unknown: number of experiments David did
Known: Michael did 5 less than 3 times the number David did; Michael did 13.

13. Solve application problems with one unknown quantity.
Example
(continued)
Step 2(a)
Assign a variable: Let n represent the number of experiments David did.
Step 3
Write an equation:

14. Solve application problems with one unknown quantity.
Example
(continued)
Step 4
Solve the equation:

15. Solve application problems with one unknown quantity.
Example
(continued)
Step 5
State the answer: David did 6 experiments.
Step 6
Check the answer:
3 times David’s number • 6 = 18
Less – 5 = 13
Michael did 13