1. Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test
Simplify: 1.
4 • 5 3
• 3 20 9
Common
Denominator + +
4 • 6 8 24
• 3 24 29
Add 29 = 5
Or 1 24 24 24 2. 8 12 ÷ 25 35
Note: To divide fractions, we invert and multiply. 2 7 8 35 14 • = 25 12 15 5 3
Note: When multiplying, reduce any numerator with any denominator.
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2. Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test
Simplify:
Note: Line up decimal points
and add.
69.03
74.12
74.12
• 0.9
Note: Having three digits behind the decimal point before you multiply means three digits should be behind the decimal point in the answer.
.47
x .9
.423
.423

3. Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test
5. a) Translate the equation:
Eight more than three times a number is 20.
3x = 20
b) Solve the equation.
3x = 20
− 8
− 8
Subtract
3x = 12
Divide 3 3
x = 4

4. Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test
6. a) Translate the inequality:
Four times the difference of a number and
three is less than 16.
4(x – 3) < 16
b) Solve the inequality.
4(x – 3) < 16
Distribute
4x – 12 < 16
+ 12
+ 12
Add
4x < 28 4 4
Divide
x < 7

5. Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test
7. The sum of 2 consecutive integers is 51.
a) Write a variable equation for the given information.
Assign variables:
Let, x = the 1st integer
and x + 1 = the 2nd integer
x + x = 51
Simplify
2x = 51
b) Find the integers.
2x = 51
The first integer is x
Subtract
− 1
− 1
1st integer:
2x = 50
Divide 2 2
The second integer is x + 1
x = 25
2nd integer: 26

6. Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test
8. Carlie Jo is 8 years younger than Gina. Tuana is one year
older than Gina. The sum of their ages is 29.
a) Write a variable equation for the given information.
Tuana is one year
older than Gina
Carlie Jo is 8 years younger than Gina
The sum of their ages is 29
Assign variables:
Let, g = Gina’s age ,
g – 8 = Carlie Jo’s age,
g = Tuana’s age
g + g – g = 29
Simplify
3g – 7 = 29
b) How old is each person?
3g – 7 = 29
Gina’s age is g
Gina is 12 yrs old
Add
+ 7
+ 7
3g = 36
Carlie Jo is g – 8
Carlie Jo is 4 yrs old
Divide 3 3
Tuana is g + 1
Tuana is 13 yrs old
g = 12

7. Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test
9. Juanita has the same number of dimes as nickels.
She has a total of $ How much of each coin does
she have?
Let, d = # of dimes,
Write an equation.
n = # of nickels,
.10d n = 1.95
Since there is the same number of dimes as
nickels, substitute n for d.
.10n n = 1.95
Multiply by 100 to eliminate decimal point
10n + 5n = 195
15n = 195
Combine 15 15
Divide
n = 13
She has 13 of each coin.

8. Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test
10. Dwayne weighs two-thirds as much as his older sister.
The sum of their weights is 90 lbs. How much does
Dwayne weigh?
Let, d = Dwayne’s weight,
Write an equation.
s = Sister’s weight,
d + s = 90
Since Dwayne weighs two-thirds as much as
his sister substitute s for d. 2 3 2
s + s = 90
Multiply by 3 to eliminate fraction 3
2s + 3s = 270
5s = 270
Combine 5 5
s = 54
Divide

9. Algebra I Concept Test # 4 – Single Variable Word Prob. Practice Test
10. Dwayne weighs two-thirds as much as his older sister.
The sum of their weights is 90 lbs. How much does
Dwayne weigh?
sister = 54 pounds
Do not let others distract you.
Be responsible for your actions.
Since Dwayne weighs two-thirds as much as
his sister, multiply her weight by two-thirds to
obtain Dwaynes weight.
D = S 2 3
D = (54) 2
Substitute 3
D = 36
Dwayne weighs 36 pounds.