WRITING EXPRESSIONS WORD PROBLEMS

Problem 1 :

Twice the product of m and n decreased by the square of the sum of m and n. Which of the following is an expression for the statement above?

(A)  2mn - (m² + n²)

(B)  2mn - (m + n)²

(C)  (m + n)² - 2mn

(D)  (m² + n²) - 2mn

Solution :

Therefore, the correct answer is option (B).

Problem 2 :

The product of a number x and four decreased by twelve. Which of the following is an expression for the statement above?

(A)  4x + 12

(B)  4(x + 12)

(C)  4(x - 12)

(D)  4x - 12

Solution :

Therefore, the correct answer is option (D).

Problem 3 :

The quotient of 19 and a number d increased by nine. Which of the following is an expression for the statement above?

(A)  ¹⁹⁄d + 7

(B)  ᵈ⁄₁₉ + 7

(C)  ⁽¹⁹ ⁺ ᵈ⁾⁄₇

(D)  ⁽ᵈ ⁺ ⁷⁾⁄₁₉

Solution :

Therefore, the correct answer is option (A).

Problem 4 :

John received y text messages each minute for 10 minutes yesterday and received t text messages each minute for 20 minutes today. What is the total number of text messages he received for two days in terms of y and t?

(A)  30yt

(B)  200yt

(C)  20y + 10t

(D)  10y + 20t

Solution :

The number of text messages Mario received yesterday :

= 10y

The number of text messages Mario received today :

= 20t

The total number of text messages he received for two days :

= 10y + 20t

Therefore, the correct answer is option (D).

Problem 5 :

Which of the following expressions represents the product of 3k and the sum of m and one third of n?

(A)  3km + (⅓)n

(B)  3k ⋅ (⅓)(m + n)

(C)  3k ⋅ [m + (⅓)n]

(D)  3k ⋅ (m + n + ⅓)

Solution :

Therefore, the correct answer is option (C).

Problem 6 :

The difference between two numbers is eight. If the smaller number is n to the third power what is the greater number?

(A)  n³ - 8

(B)  n³ + 8

(C)  8 - n³

(D)  8n³

Solution :

Let x be the greater number.

Smaller number is n to the third power. That is n³.

Given : Difference between two numbers is eight

x - n³ = 8

Add to n³ both sides.

x = 8 + n³

Greater Number = n³ + 8

Therefore, the correct answer is option (B).

Problem 7 :

Mr. and Mrs. Sawyer are taking their three children to an amusement park. The admission is a dollars per adult, c dollars per child and the cost of each ride is r dollars per person.

a. Write an expression for the cost of admission plus 10 rides for the family.

b. Find the cost of admission plus 10 rides if the admission per adult is 20 dollars, the admission per child is 12 dollars, and the cost of each ride is 8 dollars.

Solution :

Part (a) :

2a + 3c + 10r

Part (b) :

To find the cost of admission plus 10 rides, substitute 20 for a, 12 for c and 8 for r in the above expression.

= 2(20) + 3(12) + 10(8)

= 40 + 36 + 80

= $156

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