What is the sum of two numbers is 40 and their difference is 10?

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Arithmetic is a branch of mathematics that deals with numerals, number system, and their operations from ancient times. The term was originally derived from the Greek word “arithmos” which simply means numbers. It is preferred to get a definite single value. 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.

History of Arithmetic

• The 17th-century Indian mathematician Brahmagupta is the “father of arithmetic”.
• Carl Friedrich Gauss in 1801, provided the Fundamental principle of number theory.

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.

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

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 number of values is called summation.

0 is considered as the identity element of addition as while adding 0 to any value gives the same result. For example, if we add 0 to 5 the result would be the same that is 5.

0 + 3 = 3

And, the addition of 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 2 with its opposite value -5, then the result would be

5 + (-5) = 0

Subtraction (-)

The arithmetic operation 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. It is the inverse of addition.

9 – 3 = 6

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

3 – 9 = -6

Multiplication (×)

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

The product of two values supposedly x and y are expressed in x.y or x×y form.

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.

10/5 = 2

Sum of two numbers is 40 and their difference is 10. Find the numbers

Answer:

Let the two numbers be x and y.

According to the question,

x + y = 40……(i)

x – y = 10……..(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 = 40 – y

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

=>40 – y – y = 10

=>40 – 2y = 10

=>y = 30/2

=>y = 15

Substituting the value of y = 15 in x = 40 – y

=>x = 40 – 15 = 25

Hence, the two variables are x = 25 and y = 15.

Question 1: The sum of two numbers is 8 and their difference is 4. Find the variables.

Answer:

Let the two numbers be x and y.

According to the question,

x + y = 8…….(i)

x – y = 4……(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 = 4

=>8 – 2y = 4

=>-2y = -4

=>y = -4/-2 = 2

Substituting the value of y = 2 in x = 8 – y

=>x = 8 – 2 = 6

Hence, the two variables are x = 6 and y = 2.

Question 2: If the sum of two numbers is 95 and one exceeds the other by 15. What are the numbers?

Answer:

Let the two numbers be x and x + 15

Now, according to the question,

=>x + x + 15 = 95

=>2x = 95 – 15

=>2x = 80

x = 80/2 = 40

If the first number is x = 40. Then, the value of the second number is given by

=>x + 15 = 40 + 15 = 55

Therefore, the two numbers are 40 and 55.

Question 3: The sum of the two numbers is 25 and the difference is 13. Find the numbers.

Answer:

Let the two numbers be x and y.

According to the question,

x + y = 25……(i)

x – y = 13……(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 = 13

=>25 – 2y = 13

=>2y = 25 – 13

=>2y = 12

=>y = 38/2 = 6

Substituting the value of y = 6 in x = 25 – y

=>x = 25 – 6 = 19

Hence, the two variables are x = 19 and y = 6.

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

Answer:

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.

The Sum of Two Numbers is 40 and Their Difference is 10

The sum of two numbers is 40 and their difference is 10. What are the two numbers? Let's start by calling the two numbers we are looking for x and y. The sum of x and y is 40. In other words, x plus y equals 40 and can be written as equation A:

x + y = 40

The difference between x and y is 10. In other words, x minus y equals 10 and can be written as equation B:

x - y = 10

Now solve equation B for x to get the revised equation B:

x - y = 10
x = 10 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 40
10 + y + y = 40 10 + 2y = 40 2y = 30

y = 15

Now we know y is 15. Which means that we can substitute y for 15 in equation A and solve for x:

x + y = 40
x + 15 = 40
X = 25

Summary: The sum of two numbers is 40 and their difference is 10. What are the two numbers? Answer: 25 and 15 as proven here:

Sum: 25 + 15 = 40
Difference: 25 - 15 = 10

Sum Difference Calculator Do you want the answer to a similar problem? Enter the sum and difference here to find the two numbers:

The Sum of Two Numbers is 40 and Their Difference is 11

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Shatiek S.

asked • 06/04/19

2 Answers By Expert Tutors

Let's break the problem into two parts.

1. "The sum of two numbers is 40."
2. "Their difference is 10."

Your looking for two numbers that work for both parts of the sentence.

1) "The sum of two numbers is 40." The word "sum" mean to add. For this part of the problem, you'd need to think of ways to get two numbers that add up to 40. For instance, 20 + 20 = 40. Another solution would be 35 + 5 = 40, and so on.

2) Let's look at the second part of the problem. "Their difference is 10." The word "difference" mean to subtract. For this part of the problem you would need to think of two numbers whose difference is 10. for instance, 20 - 10 = 10, Another possibility is 52 - 42 = 10.

Since we are looking for two number that work with BOTH parts of the question, the correct answer is 25 and 15. Why are these the two correct numbers?

1. "The sum of two numbers is 40." 25 + 15 = 40
2. "Their difference is 10." 25 - 15 = 10

There you go! Best wishes!

Barakah Q. answered • 06/05/19

Wellesley College Computer Sci & Pol Sci, 7+ Years Tutoring

We know that x + y = 40 and x - y = 10. Since we have two equations with these values, we need to do substitution. We know that x = 40 - y. We use this x value that we have an plug it into the other equation. Thus x - y = 10 is the same as (40 - y) - y = 10. This is equal to 40 - 2y = 10. We then move around the numbers in the equation to get 2y = 30. You want to isolate the y value, so you divide by 2 and get y = 15. Now you know the value of y and you can plug it in to get the value of x. Thus x - 15 = 10, thus x = 25.