PROBLEMS ON NUMBERS WITH SOLUTIONS

Problem 1 :

Twice a number is 500 more than six times the number. What is the number?

Solution :

Let x be the required number.

From the ngiven information,

2x = 6x + 500

Subtract 6x from both sides.

-4x = 500

Divide both sides by -4.

x = -125

Therefore, the number is -125.

Problem 2 :

Three-sevenths of a number is 24. Find the number.

Solution :

Let x be the required number.

From the ngiven information,

Multiply both sides by 7.

3x = 168

Divide both sides by 3.

x = 56

Therefore, the number is 56.

Problem 3 :

What number increased by ¼ of itself is equal to 30?

Solution :

Let x be the required number.

From the ngiven information,

Multiply both sides by 4 and simplify.

4x + x = 120

5x = 120

Divide both sides by 5.

x = 24

Therefore, the number is 24.

Problem 4 :

If 6 times a number is decreased by 6, the result is the same as when 3 times the number is increased by 12. Find the number.

Solution :

Let x be the required number.

From the ngiven information,

6x - 6 = 3x + 12

Subtract 3x from both sides.

3x - 6 = 12

Add 6 to both sides.

3x = 18

Divide both sides by 3.

x = 6

Therefore, the number is 6.

Problem 5 :

If 3 times a number is increased by 22, the result is 14 less than 7 times the number. What is the number?

Solution :

Let x be the required number.

From the ngiven information,

3x + 22 = 7x - 14

Subtract 3x from both sides.

22 = 4x - 14

Add 14 to both sides.

36 = 4x

Divide both sides by 4.

9 = x

Therefore, the number is 9.

Problem 6 :

Separate 84 into two parts such that one part will be 12 less than twice the other.

Solution :

Let x be one part of 84.

If y be the other part, then

x = 2y - 12 ----(1)

Since x and y are the two parts, we have

x + y = 84

Substitute x = 2y - 12.

2y - 12 + y = 84

3y - 12 = 84

Add 12 to both sides.

3y = 96

Divide both sides by 3.

y = 32

Substitute y = 32 into (1).

x = 2(32) - 12

x = 64 - 12

x = 52

Therefore, the two parts of 84 are 52 and 32.

Problem 7 :

The difference between two numbers is 24. Find the numbers, if their sum is 88.

Solution :

Let x and y be the two numbers.

From the given information,

x - y = 24 ----(1)

x + y = 88 ----(2)

(1) + (2) :

2x = 112

Divide both sides by 2.

x = 56

Substitute x = 56 into (2).

56 + y = 88

Subtract 56 from both sides.

y = 32

Therefore, the two numbers are 56 and 32.

Problem 8 :

One number is 3 times another number. If 17 be added to each, the first resulting number is twice the second resulting number. Find the two numbers.

Solution :

Let x be one of the numbers.

Then, the other number is 3x.

From the information,

3x + 17 = 2(x + 17)

3x + 17 = 2x + 34

Subtract 2x from both sides.

x + 17 = 34

Subtract 17 from both sides.

x = 17

3x = 51

Therefore, the numbers are 17 and 51.

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