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What are two numbers that have the sum of 19 and a difference of 7?

  • Last Updated : 21 Sep, 2021

Arithmetic probably has the longest history during the time. It is a method of calculation that is been in use from ancient times for normal calculations like measurements, labeling, and all sorts of day-to-day calculations to obtain definite values. The term got originated from the Greek word “arithmos” which simply means numbers.

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

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Besides the traditional operations of addition, subtraction, multiplication, and division arithmetic also include advanced computing of percentage, logarithm, exponentiation and square roots, etc. Arithmetic is a branch of mathematics concerned with numerals and their traditional operations.



Basic Operations of Arithmetic

Arithmetic has four basic operations that are used to perform calculations as per the statement:

  • Addition
  • Subtraction
  • Multiplication
  • Division

Addition (+)

The simple definition for addition will be that it 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.

0 is said to be the identity element of addition as while adding 0 to any value it gives the same result. For example, if we add 0 to 6 the result would be the same that is 6.

0 + 6 = 6

And, the inverse element includes the addition of the opposite value. The result of adding inverse elements will be an identity element that is 0. For example, if we add 3 with its opposite value -3, then the result would be

3 + (-3) = 0

Subtraction(-)



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

5 – 2 = 3

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

2 – 5 = -3

Multiplication(×)

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

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

3 × 5 = 15

Division(÷)

The division is the operation that computes the quotient of two numbers. It is the inverse of multiplication. The two values involved in it are known as dividends by the divisor and 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

What are two numbers that have the sum of 19 and a difference of 7?

Solution:      

Let the numbers be a and b. Now, as per the situation,

                                                 a + b = 19 ……………(i)

                                          and a – b =  7 ……………(ii)

We can write, a = 19 – b, from equation .(i),

now put the value of a in equation(ii), we get,

19 – b – b = 7

19 – 2b = 7

2b = 19 – 7 = 12

So, b = 12/2 =  6

b = 6

and a = 19 – b

          = 19 – 6

      a = 13

Therefore, the two numbers are 13 and 9.

Sample Arithmetic Problems

Question 1: The sum of the two numbers is 50, and their difference is 10. Find the numbers.

Solution:

Let the numbers be a and b. Now, as per the situation,

       a + b = 50……………………(i)



and a – b = 10………………(ii)

We can write, a = 50 – b, from equation .(i),

no put the value of a in equation(ii), we get,

50 – b – b = 10

50 – 2b = 10

2b = 50 – 10 = 40

b = 40/2 = 20

b = 20

and 

a = 50 – b

   = 50 – 20

a = 30

Therefore, the two numbers are 30 and 20.

Question 2: Solve 55 + 2(27 ÷ 3) – 8

Solution:

55 + 2(27 ÷ 3) – 8

⇒ 55 + 2(9) – 8

⇒ 55 + 18 – 8

⇒ 63 – 8 = 45

Question 3: Find the value of a in the given equation a – 23 = 6.

Solution:

According to the equation,

=> a – 23 = 6

=> a = 23 + 6

=> a = 29

Therefore, the value of a is 29.

Question 4: Solve for the value of a

2a – 6(30 ÷ 6) – 10 × 2 = 24

Solution:

2a – 6(30 ÷ 6) – 10 × 2 = 24

=> 2a – 6 (5) – 10 × 2 = 24

=> 2a – 30 – 10 × 2 = 24

=> 2a – 30 – 20 = 24

=> 2a – 50 = 24

=> 2a = 24 + 50

=> 2a = 74

=> a = 37

Therefore the value of a is 37

Question 5: By using arithmetic operation, find the sum of 80 and 40 and then subtract 20 from the sum?

Solution:

Here, the sum of 80 and 40 by using the addition operation.

Sum = 80 + 40 = 120

Now, as per the question, subtract 20 from the sum,

120 – 20 = 100

Therefore, 100 is the final answer

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