Translating Words into Mathematical Symbols
1. 11 more than a number
2. A number decreased by 10
3. The product of 9 and a number
4. 10 times a number
5. A number multiplied by 3
6. One fourth of a number
7. The quotient of a number and 6
8. 7 divided by a number
Write the sentence as an equation or an inequality.
9. The product of 5 and a number x is 25.
10. 10 times a number x is greater than or equal to 50.
11. The difference between 13 and a number is 7.
12. A number increased by 2 is 4.
13. The product of 2 and a number is 4.
14. A number decreased by 4 is 2.
15. A number divided by 4 is 2
16. The sum of 20 and a number is 30.
17. A number increased by 10 is greater than or equal to 44.
18. 35 is less than the difference of 21 and a number.
19. The quotient of 49 and a number is 7.
20. 28 decreased by a number is 18.
Translate and solve the real-life problems.
21. You make a long distance telephone call. The rate is $.10 for each minute. The
total cost of the call is $5.00. How long was the call? Check to see if your
solution is reasonable.
22. You want to hire a live band for a school dance. You have $175 in your budget.
The live band charges $75 per hour and each student pays $2 admission. If
the band is to play for 3 hours, how much extra money do you need to raise?
3.1 Problem solving
Write an equation to model the situation. Then solve each problem.
1. Two packages of meat have a combined weight of 5.75 lbs. If one of the two packages weighs 3.28
pounds, how much does the other package weigh?
2. Alma caught a largemouth bass that measured 17½ inches long. Her father caught one 14½ inches
long. How much longer was Alma’s fish than her fathers?
3. Ms. Prappas ran a 5-mile race in 35 minutes. What was her average time per mile?
4. The normal July temperature in Phoenix, AZ is 106F. This is about 2.36 times that of Barrow,
AK. What is the normal high in Barrow? (round to nearest integer)
5. A cook boils 1.5 potatoes for each serving of mashed potatoes. How many servings can he make
from 18 potatoes?
6. The perimeter of an equilateral triangle is 25.5 cm. How long is each side?
7. A stack of twelve bricks is 27 inches high. How high is each brick?
8. The sum of Juanita’s age and Sara’s age is 33 yrs. If Sara is 15 years old, how old is Juanita?
9. The tallest person on the basketball team is 77¾ in. tall. This is 9½ in. taller than the shortest
player. How tall is the shortest player?
10. The diameter of Jupiter is 88,000 mi. This is about 11.1 times the diameter of Earth. What is the
diameter of Earth?
11. The distance from Baltimore to New York is 202 mi. This is 205 miles less than the distance from
Baltimore to Boston. How far is Baltimore from Boston?
3.1 Problem solving (2)
1. It costs $10 dollars to rent a DVD player and $2 for each DVD. If you have $18, how many DVDs
can you rent? (To find the number of DVDs, solve the equation 10 + 2d = 18
2. Suppose you are hired to remove the shells from peanuts. You currently have shelled (removed the
shell from) 6.5 lbs. of peanuts and you can shell 1.5 lbs. per hour. To find how much longer it will
take you to shell 11 lbs. of peanuts, solve the equation 6.5 + 1.5x = 11
3. The postal service charges $.37 for the first ounce to mail a first class letter. It charges $.23 for
each additional ounce. It cost $1.98 to mail your letter. How many ounces did your letter weigh?
4. A computer repair bill was $212.50. This included $75 for parts and $50 for each hour of labor.
How many hours did it take to repair the computer?
5. Suppose you have a 75 foot roll of paper you will use to decorate for a party. You need one piece
10 feet long. How many 4.5 foot long pieces can you get from the paper that is left over?
6. Suppose you have $15 to plant a garden. If you spend $6 on seeds, how many packs of vegetable
plants can you buy for $.75 each?
7. Suppose you make $126 selling popcorn. If your expenses were $22.50, how many $1.50 bags did
you sell?
8. Suppose you want to buy a pair of pants and several pairs of socks. The pants cost $24.95 and the
socks are $5.95 per pair. How many pairs of socks can you buy if you have $50 to spend?
Algebra IB
Ch 2 and 3a Review
1) a. Graph 
5
and –3 on the number line
2
b. Write an inequality statement comparing the two numbers.
2) List the numbers from least to greatest: -5.7, -6, -4, -5.65
3) Name the property used in the following.
3x + – 1 + 1 = 3x + 0
______________________________
4) Susan opened a savings account and deposited $32.45. The next day she deposited $15.67.
The next week she took out $20.65 from her account. Jimmy opened an account and deposited
$61.50. He withdrew $13.71 the next week and $16.43 the week after that. Whose account has
the greatest balance and what is it?
5) Evaluate
(a 2  b 2 )(a 2  b 2 )
2a 2  3ab
if a = 4 and b = 3.
6) Evaluate 3y³ + 2y² - y + 7 if y = – 4
Simplify.
7) Simplify.
8)
[2 3 + 4(7 – 3)]  8
–12 – 7 – 11 – [3 – (–9)]
9) (-2)³ · (3²) · ( – ¼ )
10)
5  82
 24  3  (2 3 )
11) 3(2y – 5) + 4y
12) 6m – 3n +
–
8m –
–
5n
13) 4x – 6y + 6 – 4x + 5y – 4
Solve for x.
14) 4x + 6 = 18
15) 5(3x – 7) = 8x + 28
16) 2x – 3 = 5 – (4 – 2x)
17) Multiply. 4(5r³ - ½ r² + 2r – 3)
18) Divide.
16a 3  4a 2  64a  36
4
15) A car traveled for ½ an hour at 55 miles per hour, the increased the speed by 10
mi/hr and traveled 1½ hour more. How far did the car go?