Problem 1 :
When three times a certain number is subtracted from 15, the result is -6. Find the number.
Solution:
Let the number be x.
15 - 3x = -6
3x = 15 + 6
3x = 21
x = 7
So, the number is 7.
Problem 2 :
Five times a certain number, minus 5, is equal to 7 more than three times the number. What is the number?
Solution:
Let the number be x.
5x - 5 = 7 + 3x
5x - 3x = 7 + 5
2x = 12
x = 6
So, the number is 6.
Problem 3 :
Three times the result of subtracting a certain number from 7 gives the same answer as adding eleven to the number. Find the number.
Solution:
Let x be the number.
3(7 - x) = x + 11
21 - 3x = x + 11
4x = 10
x = 10/4
x = 5/2
Problem 4 :
I think of a number. If I divide the sum of 6 and the number by 3, the result is 4 more than one quarter of the number. Find the number.
Solution:
So, the number is 24.
Problem 5 :
The sum of two numbers is 15. When one of these numbers is added to three times the other, the result is 27. What are the numbers?
Solution:
Let two numbers are x and y.
x + y = 15
x = 15 - y ---> (1)
x + 3y = 27 ---> (2)
Substitute x = 15 - y in (2)
(15 - y) + 3y = 27
15 + 2y = 27
2y = 27 - 15
2y = 12
y = 6
By applying y = 6 in (1)
x + 6 = 15
x = 15 - 6
x = 9
Problem 6 :
What number must be added to both the numerator and the denominator of the fraction 2/5 to get the fraction 7/8?
Solution:
Let the number be x.
Problem 7 :
What number must be subtracted from both the numerator and the denominator of the fraction 3/4 to get the fraction 1/3?
Solution:
Let the number be x.
Problem 8 :
Eli is now one-quarter of his father's age and in 5 years time his age will be one-third the age of his father. How old is Eli now?
Solution:
In 5 years,
Eli is 10 years now, and his father is 40 years.
Problem 9 :
When Maria was born her mother was 24 years old. At present Maria's age is 20% of her mother's age. How old is Maria now?
Solution:
Let the ages of Maria and her mother be x and x + 24 respectively.
x = 0.2(x + 24)
x = 0.2x+4.8
x - 0.2x + 4.8
0.8x = 4.8
x = 4.8/0.8
x = 6
Therefore, the present age of Maria is 6 years.
Problem 10 :
Five years ago Jacob was one-sixth the age of his brother. In three years time his age doubled will match his brother's age. How old is Jacob now?
Solution:
Let J = Jacob's current age
Let B = brother's current age
3 years from now
Jacob's age is J + 3
brother's age is B + 3
2(J + 3) = B + 3
2J + 6 = B + 3
2J - B = -3 ---> (2)
Subtract equation (2) from (1)
4J = 28
J = 28/4
J = 7
So, Jacob is 7 years old.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM