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If one number exceeds another by 5 and the sum of the numbers is 1, find the numbers

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A Number system or numeral system is defined as an elementary system to express numbers and figures. It is a unique way of representing numbers in arithmetic and algebraic structure. In various arithmetic values Numbers are applicable to carry out various arithmetic operations like addition, subtraction, multiplication, etc which are applicable in daily lives for the purpose of calculation. The numbers value is determined by the digit, its place value in the number, and the base of the number system. It is also known as Numerals are the mathematical values used for counting, measurements, labeling, and measuring fundamental quantities. 

These are the mathematical values or figures used for the purpose of measuring or calculating quantities. It is represented by numerals as 3, 6, 9, etc. Some examples of numbers are integers, whole numbers, natural numbers, rational and irrational numbers, etc.

One number exceeds another by 5. The sum of the numbers is 1. What are the numbers?

Solution: 

Let one number be x

Another number will be, x + 5

Sum of these number are 1,

x + x + 5 = 1

2x + 5 = 1

2x = 1 – 5

 2x = -4

x = -2

Then, x + 5 will be,

= x + 5

= -2 + 5

= 3

So, the numbers are -2 and 3

Similar Problems

Question 1: One number exceeds another by 7. The sum of the numbers is 1. What are the numbers?

Solution:

Let one number be x

Another number will be, x + 7

Sum of these number are 1,

x + x + 7 = 1

2x + 7 = 1

2x = 1-7

2x = -6

x = -3

Then, x + 7 will be,

= x + 7

= -3 + 7

= 4

So, the numbers are -3 and 4

Question 2: One number exceeds another by 4. The sum of the numbers is 8. What are the numbers?

Solution:

Let one number be x

Another number will be, x + 4

Sum of these number are 8,

x + x + 4 = 8

2x + 4 = 8

2x = 8 – 4

2x = 4

x = 2

Then, x + 4 will be,

= x + 4

= 2 + 4

= 6

So, the numbers are 2 and 6

Question 3: One number less another number by 5. The sum of the numbers is 9. What are the numbers?

Solution:

Let one number be x

Another number will be, x – 5

Sum of these number are 9,

x + x – 5 = 9

2x – 5 = 9

2x = 9 + 5

2x = 14

x = 7

Then, x – 5 will be,

= x – 5

= 7 – 5

= 2

So, the numbers are 7 and 2

Question 4: One number less another number by 4. The sum of the numbers is 8. What are the numbers?

Solution:

Let one number be x

Another number will be, x – 4

Sum of these number are 8,

x + x – 4 = 8

2x – 4 = 8

2x = 8 + 4

2x = 12

x = 6

Then, x – 4 will be,

= x – 4

= 6 – 4

= 2

So, the numbers are 6 and 2

Question 5: One number exceeds another by 4. The sum of the numbers is 10. What are the numbers?

Solution: 

Let one number be x

Another number will be, x + 4

Sum of these number are 10

x + x + 4 = 10

2x + 4 = 10

2x = 10 – 4

2x =  6

x = 3

Then, x + 4 will be,

= x + 4

= 3 + 4

Other number is  = 7

So, the numbers are 3 and 7

Question 6: One number is twice the other number and exceeds by 5. The sum of the numbers is 8. What are the numbers?

Solution: 

Let one number be x

Another number will be, 2x + 5

Sum of these number are 8,

x + 2x + 5 = 8

3x + 5 = 8

3x = 8 – 5

3x = 3

x = 1

Then, 2x + 5 will be,

= 2x + 5

= 2 (1)+ 5

= 7

So, the numbers are 1 and 7

Question 7: One number is twice the other number and exceeds by 5. The sum of the numbers is 11. What are the numbers?

Solution: 

Let one number be x

Another number will be, 2x + 5

Sum of these number are 11,

x + 2x+ 5 = 11

3x + 5 = 11

3x = 11 – 5

3x = 6

x = 2

Then, 2x + 5 will be,

= 2x + 5

= 2 (2)+ 5

= 9

So, the numbers are 2 and 9


Last Updated : 25 Dec, 2023
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