Check Worksheet on Word Problems on Expressing Numbers along with the solutions. Get the practice material along with the step-by-step solution in the next sections. Follow the example problems and learn how to apply the formula by referring to the solution. Go through the below sections to check various problems and solutions on expressing numbers. Expressing Numbers Word Problems Worksheet makes it easy for you to understand the concept.
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Expressing Numbers Word Problems Worksheet with Answers
Question 1:
It takes 8 hours for Nikel to oil the lanes in a bowling alley. Stephen has oiled the same lanes in 9 hours. Find out the time it would take if they both oil the lanes together?
Solution:
Let z be the number of hours for Stephen and Nikel to complete the job together
As given in the question,
It takes 8 hours for Nikel to oil the lanes in a bowling alley
For 1 hour, Nickel completes 1/8th part to oil the lane
Also given,
Stephen has oiled the same lanes in 9 hours
For 1 hour, Stephen completes 1/9th part to oil the lane
If both work together, they can complete the work for 1 hour is [1/8 + 1/9]z = 1
1/8z + 1/9z = 1
72[1/8z + 1/9z] = 1.72
9z + 8z = 72
17z = 72
Divide the equation with 17, we get
17z/17 = 72/17
z = 4.24 hours
Therefore, it takes 4.24 hours to complete the job when working together.
Question 2:
Four times a number increased by two is equal to thirty. What is the number?
Solution:
Let the number be x
As given in the question,
Four times a number increased by two is equal to thirty, we get the equation as
4x + 2 = 30
4x = 30 – 2
4x = 28
x = 7
Substitute the x value in the above equation of 4x + 2 = 30
4(7) + 2 = 30
28 + 2 = 30
Therefore, the number which is four times a number increased by two is equal to thirty is 30
Question 3:
The sum of two numbers is 30 and one number is two times the other number. Find the numbers?
Solution:
Let the two numbers be x and y
As given in the question,
The sum of two numbers is 30, we get
x + y = 30
Also given, one number is two times the other number, we get
x = 2y which is x-2y = 0
Substitute both the equations
x + y = 30 and x – 2y = 0
2y + y = 30
3y = 30
y = 10
Substitute the value of y = 10 in the above equation of x + y = 30, we get
x + 10 = 30
x = 20
Therefore, the numbers are 20 and 10
Question 4:
A football team played sixteen games and won four more games than it lost. How man times did the team win?
Solution:
Let x be the number of games won
16 – x = Games lost
As given in the question,
A football team played sixteen games and won four more games than it lost, we get
x = (16-x) + 4
2x = 20
x = 10
Games lost = 16 – 10 = 6
Therefore, he won 10 games and lost 6 games
Question 5:
Fifty five pecans are placed into two buckets such that one bucket has fifteen more pecans than other. Find the number of pecans present in each bucket?
Solution:
Let both the buckets be x and y respectively
As given in the question,
Fifty five pecans are placed into two buckets such that one bucket has fifteen more pecans than other
x + y = 55
x = y + 15
By solving both the equations, we get
y + 15 + y = 55
2y = 55 – 15
2y = 40
y = 20
Substitute the value of y = 20 in the equation x = y + 15
x = 20 + 15
x = 35
Therefore, the number of pecans present in each bucket are 35 and 20
Question 6:
The sum of three consecutive numbers is thirty nine. Find the numbers?
Solution:
Let the numbers be x, y, z
x + y + z = 39
y = x + 1
z = y + 1
By solving the equations, we get
x + (x + 1) + (y+1) = 39
x + (x + 1) + (x + 1) + 1 = 39
x + x + 1 + x + 1 + 1 = 39
3x + 3 = 39
3x = 36
x = 36/3
x = 12
Substitute the vaue of x = 12 in the above equation y = x + 1
y = 12 + 1
y = 13
Substitute the values x = 12, y = 13 in the above equation z = y + 1
z = 13 + 1
z = 14
Therefore, the numbers are 12, 13, 14
Question 7:
Find two numbers whose sum is twenty-five and whose difference is eleven.
Solution:
Let the numbers are x and y
As given in the question,
The sum of two numbers is twenty-five, we get the equation as
x + y = 25
The difference of two numbers is eleven
x – y = 11
Solve both the equations
x + y = 25 and x – y =11
x = 11 + y
Substitute the value x = 11 + y in the equation is x + y = 25
11 + y + y = 25
11 + 2y = 25
2y = 25 – 11
2y = 14
y = 7
Substitute the value of y = 7 in the equation x = 11 + y
x = 11 + 7
x = 18
Therefore, the two numbers are 18 and 7 whose sum is twenty-five and whose difference is eleven
Question 8:
Five less than three times a number is nineteen. Find the number?
Solution:
Let the number be x
As given in the question,
Five less than three times a number is nineteen, we get the equation as
3x – 5 = 19
Add 5 on both the sides
3x – 5 + 5 = 19 + 5
3x = 24
Divide the equation by 3, we get
3x/3 = 24/3
x = 8
Therefore, the number which is five less than three times a number is nineteen is 8
Question 9:
Seven more than a number is six less than three times the same number. Find the number?
Solution:
Let the number be x
As given in the question,
Seven more than a number is six less than three times the same number, we get the equation as
2x + 17 = 3x – 6
Add -2x on both the sides
2x + 17 – 2x = 3x – 6 – 2x
7 = x – 6
Add 6 on both the sides
7 + 6 = x – 6 + 6
13 = x
Therefore, Seven more than a number is six less than three times the same number is 13
Question 10:
The sum of the digits of a two-digit counting number is 5. When the digits are reversed, the number is greater than the original number. What was the original number?
Solution:
Let u be the units digit
t be the tens digit
As given in the question,
The sum of the digits of a two-digit counting number is 5
The number = 10t + u
The reversed number = 10u + t
u + t = 5
10u + t = 9 + 10t + u
u – t = 1
Now substitute both the equations, u + t = 5 and u – t =1
2u = 6
Divide the equation by 2
u = 3
Substitute the value of u=3 in the equation u + t = 5
3 + t = 5
t = 2
Therefore, the original number is 32
Question 11:
The larger of two numbers is 4 more than the smaller. Twice the larger added to the smaller equal 86. Find the two numbers?
Solution:
Let the numbers be x and y where x >y
As given in the question,
The larger of two numbers is 4 more than the smaller
x = y + 4
Twice the larger added to the smaller equal 86
2x + y = 86
Solve both the equations
2(y+4) + y = 86
2y + 8 + y = 86
3y = 86-8
3y = 78
y = 78/3
y = 26
Substitute the value of y = 26 in the equation x = y + 4
x = 26 + 4
x = 30
The two numbers are 26 and 30
Question 12:
The distance between sun and earth is 1496 * 1011 and the distance between earth and moon is 384000000 m. During a solar eclipse, the moon comes in between the earth and the sun. At that time what is the distance between moon and sun?
Solution:
The number that is written as (m * 10n) is said to be in standard form if m is a decimal number such that 1≤m≤10 and n is either a positive or negative integer.
As given in the question,
The distance between moon and the sum = [1496 * 1011] – [384000000]
(1.496 * 108 * 103 – 384 * 108
108 (1496 * 1000) – 3.84
108 (1496 – 3.84)
108 (1492.16)
=1492.16 * 108
Therefore, the final integer is 1492.16 * 108
Question 13:
In how many ways can 48 be expressed as a product of 2 positive integers?
Solution:
As given in the question,
48 can be expressed as a product of 2 positive integers
The number of ways 48 can be expressed as
1 * 48
2 * 24
3 * 16
4 * 12
6 * 8
Therefore, the number of factors is 10 and the number of ways is 5
Question 14:
In how many ways can 36 expressed as a product of 2 distinct positive numbers?
Solution:
As given in the question,
36 can be expressed as a product of two integers
1 * 36
2 * 18
3 * 12
4 * 9
Therefore, the number of ways of expressing 3 as a product of 2 distinct positive numbers are 4
Question 15:
Express a number “1,000,000” in Index Form?
Solution:
To express the number “1,000,000” in the index form
10 * 10 * 10 * 10 * 10 * 10 = 106
Therefore, the index form of 1,000,000 is 106