**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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