2. 3.3 Solving Application Problems with One Unknown Quantity
Chapter 3 Solving Application Problems

3. 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.
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4. Objective 1: 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
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5. Objective 1: 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
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6. Objective 2: 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.
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7. Objective 2: Translate sentences into equations.
(continued)
Example
Check
We see that 5 • = = 26.
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8. Objective 3: Solve application problems with one unknown quantity.
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9. Objective 3: Solve application problems with one unknown quantity.
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?
Example
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
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10. Objective 3: Solve application problems with one unknown quantity.
(continued)
Example
Step 2(a)
Assign a variable: Let m represent the money at the start.
Step 3
Write an equation:
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11. Objective 3: Solve application problems with one unknown quantity.
(continued)
Example
Step 4
Solve the equation:
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12. Objective 3: 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
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13. Objective 3: Solve application problems with one unknown quantity.
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?
Example
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.
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14. Objective 3: Solve application problems with one unknown quantity.
(continued)
Example
Step 2(a)
Assign a variable: Let n represent the number of experiments David did.
Step 3
Write an equation:
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15. Objective 3: Solve application problems with one unknown quantity.
(continued)
Example
Step 4
Solve the equation:
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16. Objective 3: Solve application problems with one unknown quantity.
(continued)
Example
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
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