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Sum of two numbers is 7 and their difference is 1. Find the numbers

  • Last Updated : 17 Aug, 2021

The 17th-century Indian mathematician Brahmagupta is the “father of arithmetic” and Carl Friedrich Gauss in 1801, provided the Fundamental principle of number theory. Arithmetic is elementary of mathematics that is majorly concerned with numerals,  number system, their properties, and their operations from ancient times. The term is derived from the Greek word “arithmos” which simply means numbers. The traditional methods of arithmetic operations are constituent of addition, difference, multiplication, and division. These operations are being carried out for the purpose of human social and economical development for centuries.

The branch of mathematics that specifically deals with the study of numbers and properties of traditional operations like addition, subtraction, multiplication, and division is called as Arithmetic.

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Besides the traditional operations of addition, subtraction, multiplication, and division arithmetic also include advanced calculating methods for percentage, logarithm, exponentiation and square roots, etc.



Types of Basic Operation in Arithmetic

The four basic operations of arithmetic are discussed below:

Addition(+)

Addition or also known as summation is an operation to combine two or more values or numbers into a single value. The process of adding n numbers of value is called summation.

While adding 0 to any value gives the same result. Hence, 0 is known as the identity element of addition. For example: if we add 0 with 1 the result will still be 1.

0 + 1 = 1

Whereas, when we add the opposite value of the same number is said to be an inverse element. The result of the addition of inverse elements is an identity element that is 0. For example, if we add 1 with its opposite value -1, then the result would be

1 + (-1) = 0

Subtraction(-)



Subtraction is the inverse of addition. It is the arithmetic operation that determines the difference between two values (i.e. minuend minus the subtrahend) is subtraction. In the cases, where the minuend is greater than the subtrahend, the difference is positive.

5 – 2 = 3

While, if the subtrahend is greater than minuend the difference between them will be negative.

2 – 5 = -3

Multiplication (×)

The operation which combines two values to give a single product of them is called multiplication. The two values involved in the operation of multiplication are known as multiplicand and multiplier.

The product of two values is supposedly p and q is expressed in p.q or p×q form.

Division (÷)

The division is the inverse of multiplication. It is the operation that computes the quotient of two values. The two values involved in it are known as dividends by the divisor. If the quotient is more than 1, if the dividend is greater than the divisor the result would be a positive number.

9/3 = 3



Now, let’s jump onto the question,

What two numbers have a sum of 7 and a difference of 1?

Answer:

Let the two numbers be x and y.

According to the question,

x + y = 7……(i)

x – y = 1…….(ii)

Now, to know the value of one of the variables we need to solve one of the equations given above and substitute the value in the other equation.

Now, from equation (i) we can obtain the value of x by isolating it.

=>x = 7 – y

Then, substituting the value of x in equation (ii)

=>7 – y – y = 1

=>7 – 2y = 1

=>2y = 7 – 1

=>y = 6/2 = 3

Substituting the value of y = 3 in x = 7 – y

=>x = 7 – 3 = 4

Hence, the two variables are x = 4 and y = 3.

Similar Questions

Question 1: The sum of two numbers is 8 and their difference is 2. Find the variables.

Solution:

Let the two numbers be x and y.

According to the question,

x + y = 8……(i)

x – y = 2…….(ii)

Now, to know the value of one of the variables we need to solve one of the equations given above and substitute the value in the other equation.

Now, from equation (i) we can obtain the value of x by isolating it.

=>x = 8 – y

Then, substituting the value of x in equation (ii)

=>8 – y – y = 2

=>8 – 2y = 2

=>2y = 8 – 2



=>y = 6/2 = 3

Substituting the value of y = 3 in x = 8 – y

=>x = 8 – 3 = 5

Hence, the two variables are x = 5 and y = 3.

Question 2: Let’s take two numbers whose sum is 11 and their product is 30. Find the value of numbers.

Solution:

Let the two numbers be x and y.

Now, according to the question,

x + y = 11……(i)

x.y = 30…….(ii)

Now, from equation (ii) we can obtain the value of x by isolating it.

=>x = 30/y

Then, substituting the value of x in equation (i)

=>30/y + y = 11

=>30 + y2 = 11y

=>y2 – 11y + 30 = 0

=>y2 – 6y – 5y + 30 = 0

=>y(y – 6) – 5(y – 6) = 0

=>(y – 6)(y – 5) = 0

=>y = (5, 6)

=>x = (6, 5)

Question 3: The sum of the two numbers is 8 and the sum of their reciprocal is 8/15. Find the numbers.

Solution:

Let the two numbers be x and y.

According to the question,

x + y = 8…….(i)

1/x + 1/y = 8/15…….(ii)

Now, to know the value of one of the variables we need to solve one of the equations given above and substitute the value in the other equation.

Now, from equation,

=>8/xy = 8/15

=>xy = 15

=>x = 15/y

Then, substituting the value of x in equation (i)

=>15/y + y = 8

=>15 + y2 = 8y

=>y2 – 8y + 15 = 0

=>(y – 5)(y – 3) = 0

=>y = (5, 3)

=>x = (3, 5)

Question 4: If the sum of two non-zero numbers is 8 and their difference is 7. Find the value of numbers.



Solution:

Let the two numbers be x and y.

According to the question,

x + y = 25……(i)

x – y = 7…..(ii)

Now, to know the value of one of the variables we need to solve one of the equations given above and substitute the value in the other equation.

Now, from equation (i) we can obtain the value of x by isolating it.

=>x = 25 – y

Then, substituting the value of x in equation (ii)

=>25 – y – y = 7

=>25 – 2y = 7

=>2y = 25 – 7

=>2y = 18

=>y = 18/2 = 9

Substituting the value of y = 9 in x = 25 – y

=>x = 25 – 9 = 16

Hence, the two variables are x = 16 and y = 9.




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