WORD PROBLEMS

Translating English phrases with Mathematical

operations• “A number n increased by 3”

• “Three less than a number y”

• “Two times the sum of a number x and 3”

• “Twelve divided by a number p”

• “A number y exceeds two times a number x by 5”

• “The sum of a number x and 3 is at least 7”

• “When 2 is subtracted from a number n, the difference is at most 5”

n + 3

y = 2x + 5

2(x+3)𝟏𝟐𝒑

y – 3

x +3 ≥ 7

n – 2 ≤ 5

LESS, LESS THAN, & IS LESS THAN

x less y : x – yx less than y : y – xx is less than y : x y

Easy Practice Time

1. 5 is less than x.

2. A number p is increased by 7

3. A number y exceeds 3 times a

number x by 2

4. 10 less than 3 is how much?

5. 5 times the sum of a number x and 10

5

P + 7

Y = 3x + 2

3 – 10 = -7

5 (x + 10)

SAT format Practice Time1. Carl has 7 fewer than twice the

number of course credits that Steve has. Steve has 5 more credits than Gary. If Gary has 8 course credits, how many does Carl have?

A. 6B. 19C. 29D. 27E. 33

SAT format Practice Time2. Which of the following expressions

represents the phrase “3 less than 2 times x”?

A. 3 – 2xB. 2 – 3xC. 3x – 2 D. 2x – 3 E. 2 (3 – x)

SAT format Practice Time3. When 4 times a number n is increased

by 9, the result is 21.

Which of the following equations represents the statement above?

A. 4 (n+9) = 21B. 4n = 9 + 21C. n + 4 X 9 = 21D. 4n + 9 - 21E. 4 + 9n = 21

SAT format Practice Time4. If x – 4 is 2 greater than y + 1, then

by how much is x + 6 greater than y?

A. 7B. 8C. 13D. 14E. 15

SAT format Practice Time5. When 3 is subtracted from 5 times a

number n, the result is 27.

Which of the following equations represents the statement above?

A. 5n – 3 = 27B. 3n – 5 = 27C. 5 (n – 3) = 27D. 3 (n – 5) = 27E. 3 – 5n = 27

SAT format Practice Time6. If of a number is 4 less than of the

number, the number is?

A. 12B. 18C. 24D. 30E. 36

SAT format Practice Time7. Susan weighs P pounds. If Susan

gains 17 pounds, she will weigh as much as Carol, who weighs 8 pounds less than Judy. If Judy weighs X pounds, then Susan’s weight, p, in terms of x is?

A. X – 25 B. X – 9 C. X + 9D. 17X - 8E. X + 25

SAT format Practice Time8. When 2 times a number n is

decreased by 5, the result is at least 11.

Which of the following equations represents the statement above?

A. 2 (n- 5) B. 2n – 5 C. 2n – 5 11D. 2n – 5 = 11E. 2 (n-5) 11