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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
2.4 Basic Operations With Variables - Word Problems - 4

Example 1:
The reciprocal of a number is equal to 1/25 of that number. If the number is positive, what is its value?
Translate the statement to a math equation, and then solve the equation.
Let the number be n
"The reciprocal of a number" translates to 1/n.
"Is equal to 1/25 of that number" translates to 1/9 x n = n/9
Therefore the equation is 1/n = n/25
Solving for n we get: 1/n = n/25
n2 = 25
n = 5

Example 2:
Six times the reciprocal of a number is equal to that number decreased by 1. What is the number?
Solution:
Translate the statement to a math equation, and then solve the equation.
Let the number be n.
Its reciprocal is 1/n.
Six times the reciprocal of a number translates to 6 x 1/n = 6/n
That number decreased by 1" translates to n - 1
Therefore the equation is 6/n = n - 1
Solving the equation to get the value of n:
6/n = n - 1
6/n = (n - 1)/1
6(1) = n(n-1)
6 = n2 - n
n2 - n - 6 = 0 is a quadratic equation with two values n = 3 and n= -2

Directions: Solve the unknown for the following word problems.
Q 1: The reciprocal of a number is equal to 1/9 of that number. If the number is positive, what is its value?
(Hint: 1/n = n/9 Therefore n = ____)
9
6
3

Q 2: Eight time the reciprocal of a number minus 2 is equal to 2. What is the number?
(Hint: 8 x 1/n - 2 = 2 Therefore n = _____)
n = 2
n = 3
n = 4

Q 3: The reciprocal of a number is equal to 1/4 of that number. If the number is positive, what is its value?
(Hint: 1/n = n/4 Therefore n = ____)
3
2
4

Q 4: Nine less than a number squared is equal to 16. If this number is positive, what is its value?
(Hint: n2 - 9 = 16)
4
6
5

Q 5: Ten less than a number squared is equal to 110. If this number is positive, what is its value?
(Hint: n2 - 10 = 100)
10
100
9

Q 6: Six times the reciprocal of a number is equal to 24. What is the number?
(Hint: 6 x 1/n = 24 that is same as 6/n = 24 Therefore n = _____)
n = 5
n = 4
n = 1/4

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Question 8: This question is available to subscribers only!


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