## Sep 30, 2009

### Algebraic Equations: Single Variable

This post contains word problems from algebraic equations in single variable. All problems are based on relationships in numbers.
1.   Thrice the sum of a number and 2 equals 24 added with the same number. Write algebraic equation and find the number.

Solution:
Let x be the number.
For the given statement, we have following algebraic equation
3* (x+2) =24+x
3 x + 6= 24 +x
Subtracting x on both sides,
2x +6 = 24
Subtracting 6 on both sides,
2x= 18
Dividing by 2,
X=9
Therefore, the 9 is the number.

2.   Consider three consecutive positive integers. If the third number is subtracted from the sum of first two numbers, the difference is 10. Find the numbers.

Solution:
Let x, x+1 and x+2 be the three consecutive positive numbers.
X +(x+1)-(x+2) =10
2x +1-x-2=10
x- 1 = 10
Adding 1 on both sides,
X=11
Therefore, the three numbers are 11, 12 and 13.

3.   A number added with thrice a number is 20. Convert this statement into algebraic equations and find the number.

4.   A number divided by 7 is five-fourteenth. Find the number.

5.   Sum of a number and 15 is 96. Find the number.

6.   The difference of two numbers is 100. If one of the numbers is 91, find the other number.

7.   12 less than twice a number is 20. Find the number.

8.   If a number is subtracted from 32, the digits of 32 are interchanged. Write the statement as algebraic equation and also find the number.

9.   The difference of 5 times a number and 17 is 23. Find the number and 5 times the number.

10.  One-third of a number minus seven gives eight. Find the number.

11.  Consider two-third of number and add up six to it. The result is ten. Find the unknown number.

12.   I think of a number. If I subtract 6 from the number and divide it by 13, I will get the result as 2. Find the number in my mind.

13.   Wilson has a number in mind. If he takes away one-third of the number from it the result is sixteen-third. Find the number.

14.  The sum of two consecutive numbers is 19. Find the numbers and its difference.

15.  The sum of three consecutive numbers is 18. Find the numbers and check your answer.

16.  The sum of two consecutive odd numbers is 20. Find the numbers.

17.  The sum of two consecutive even numbers is 198. Find the numbers and its product.

18.  The sum of three consecutive odd numbers is 81. Find the numbers and check your answer.

19.  The sum of three consecutive even numbers is 42. Choose suitable variable and create single variable algebraic equations and find the difference between the greatest and smallest number.

20.  One-third of certain number added with one-fifth of the same number gives eight-fifteenth of the number. Find the number and check your calculation.

21.   The difference between one-third of a number and 5 is 10. Find the number.

22.   The sum of two numbers is 132, whose ratio is 5:6. Find the numbers.

23.   The sum of the digits of a two digit number is 15. If the digits in the tenth place 8, find the two digit number.

24.    If twice a number is subtracted from 97, the digits of 97 are interchanged. Find the number.

25.   Find the fraction whose numerator is 3 and the denominator is 1 more than twice the numerator.

26.   The difference of two numbers is 70. If the larger number is 6 times the smaller number, find the numbers.

27.  Two numbers are in the ratio 1:3. If I add 2 to each of the numbers, the ratio becomes 1:2. Find the original numbers.

28.   The sum of 7 more than 5 times a number is equal to sum of 6 more than twice the same number. Write the statement into possible algebraic equations and find the unknown number.

29.   A number equals 5 times the difference between the number and 4. Find the number.

30.   In a fraction, the denominator is 3 more than numerator. The sum of numerator and denominator is 7. Find the fraction.
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