Question #1

The sum of two numbers is 44, and the larger number is 2 more than the smaller number. What is the smaller number?

If x = the smaller number and y = the larger number, then which of the following systems of equations represents the word problem?

A.x + y = 44 and y = x + 2

B.x + y = 44 and y = 2x

C.x + y = 44 and x = y + 2

Question #4

The sum of Pete's and Sam's ages is 30. Five years ago, Pete was 3 times as old as Sam. How old is Sam?

Let P = Pete's age, S = Sam's age, and P + S = 30. Which of the following equations would complete the system?

A.P - 5 = 3S

B.P - 5 = 3S - 5

C.P - 5 = 3S - 15

Question #2

The sum of two numbers is 95. If the larger number is increased by twice the smaller number, the result is 120. What is the larger number?

If x = the smaller number and y = the larger number, then which of the following systems of equations represents the word problem?

A.x + y = 95 and x + 2y = 120

B.x + y = 95 and 2x + y = 120

C.x + y = 95 and 2(x + y) = 120

Question #6

The sum of the two digits of a number is 16. The number formed by reversing the digits is 18 more than the original number. Determine the original number.

Let t = the tens digit, u = the units digit, and u + t = 16. Which of the following equations would complete the system?

A.9t - 9u = 18

B.9u - 9t = 18

C.tu = ut + 18

Question #3

John is twice as old as Mary. The sum of their ages is 21. How old is Mary?

Let J = John's age and M = Mary's age. Select the system equations that represents the problem.

A.J - 2M = 0

B.M - 2J = 0

C.J + M = 21

D.J = M + 2

Question #7

The ratio of the numerator to the denominator of a fraction is 2 to 3. If both the numerator and the denominator are increased by 2, the fraction becomes 3/4. What is the original fraction?

Which of the following systems of equations can be used to solve the problem?

A.n + 4 = 3 and d + 5 = 4

B.3n - 2d = 0 and 4n + 2 = 3d + 2

C.3n = 2d and 4n + 8 = 3d + 6

Question #9

If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1.

What is the numerator of the fraction?

A.2

B.9

C.16

Question #8

If the numerator of a fraction is increased by 3, the fraction becomes 3/4. If the denominator is decreased by 7, the fraction becomes 1. Determine the original fraction.

Which of the following equations represents "If the numerator of a fraction is increased by 3, the fraction becomes 3/4"? (Hint: cross products)

A.3n + 9 = 4d

B.4n + 3 = 3d

C.4n + 12 = 3d

[] Question #5

The sum of the two digits of a number is 9. If the tens digit is one-half the units digit, what is the number?

Let t = the tens digit, u = the units digit, and t + u = 9. Which of the following equations would complete the system?

A.t =1/2 u

B.u =1/2 t

C.t - u =1/2

Relevance

1a

4c

2b

6b

3c

7c

9b

8c

5a

• Anonymous

I'm not doing all of your homework for you, let alone for free. But I'll give you some help.

1) If x is the smaller number and y is the larger number, then "the sum of the two numbers is 44" means x+y=44. "The larger is 2 more than the smaller" means y = x+2. Sole the system to find x, the smaller number.

4) We already know that P+S=30 because "The sum of Pete's and Sam's ages is 30". Now we just need to translate the "Five years ago, Pete was 3 times as old as Sam" part. If P and S are their present ages, then five years ago their ages were P-5 and S-5. So set "P-5" to be 3 times "S-5".