# What two numbers have a sum of 29 and a difference of 5?

Representation of quantities can be done with the help of numbers and figures. But for the calculation and interrelation purpose, we need different mathematical operators. For example, we can represent two baskets filled with mangoes and there are 5 mangos in the first basket and 6 mangos in the second basket. If someone asked, How many mangos are there in total? Then we can count them all and tell the answer but to make the whole process easy we introduce addition operators. We can easily add them and tell the final answer. So to reduce the complication and make the process simple we introduce mathematical operators.

Following are different types of mathematical operators.

**Addition:**It is represented by ‘+’ sign and used for the addition of two or different objects.**Subtraction:**It is represented by ‘-‘ sign and used to subtract two or different objects.**Multiplication:**It is represented by ‘×’ sign and used to multiply two or different objects.**Division:**It is represented by ‘÷’ sign and it is used for the division of two objects.

**What is Summation?**

Summation is the process of the addition of two or more numbers to get the result. For example, when 2 and 5 are added then we will get the result as 7. The addition is the primary mathematical operator. The number which we add is called as addend and the answer which we got after addition is called ‘sum’.

**What is Subtraction?**

Subtraction is the process in which we find the difference between two numbers. For example, when 2 is subtracted from 5 then we got the answer 3. It means that 5 is three more than 2. The number which we subtract is called as ‘subtrahend’ and the number from which it is subtracted is called as ‘minuend’ and the answer which we got is called as ‘difference’.

**How to Solve Equation Problems?**

The problem can be solved by using

- Single Variable Equation
- Double Variable Equation

**Single Variable Equation: **Here sum and difference of two numbers is given. Get the data from the first condition and put these values in the second condition.

**Step 1: **The sum of two numbers is given. Suppose the first number be ‘x’ then the other number be ‘sum – x’.

**Step 2: **Since we got the two numbers, now put these values in the second condition.

**Step 3:** Form an equation and solve them to get the value of x.

**Step 4:** To get the other number, subtract ‘x’ from the sum.

**Double Variable Equation: **In this method, form two-equation using the first and second conditions. Solve them and get the values of two variables.

**Step 1:** Suppose the numbers be ‘x’ and ‘y’.

**Step 2:** According to the first condition Sum of these two is given, so form an equation.

**Step 3:** Their difference is also given, so form the second equation by subtracting them.

**Step 4:** Now solve equation 1 and equation 2 to get the value of x and y.

### What two numbers have a sum of 29 and a difference of 5?

**Solution: **

Using method 1(Single Variable):According to the first given condition,

Sum of two number is 29.

Suppose one number is ‘x’ and other is ’29-x’.

According to second given condition,

Difference of these two is 5.

x – (29 – x) = 5

x – 29 + x = 5

2x = 5 + 29

2x = 34

x = 34/2

x = 17

So the one number is 17 and other number is 29 – 17, i.e. 12.

Using method 2 (Double Variable):Suppose the number is ‘x’ and ‘y’

According to the first given condition,

Sum of two number is 29.

x + y = 29 …(i)

According to second given condition,

Difference of two number is 5.

x – y = 5 …(ii)

On adding equation (i) and (ii),

x + y + x – y = 29 + 5

2x = 34

x = 34/2

x = 17

Now putting the value of x in equation (i),

17 + y = 29

y = 29 – 17

y = 12

The two number having sum 29 and difference 5 are 17 and 12.

### Similar Questions

**Question 1: What two numbers have a sum of 20 and a difference of 12?**

**Solution:**

Using method 1 (Single Variable):According to the first given condition,

Sum of two number is 20.

Suppose one number is ‘x’ and other is ’20 – x’.

According to second given condition,

Difference of these two is 12.

x – (20 – x) = 12

x – 20 + x = 12

2x = 12 + 20

2x = 32

x = 32/2

x = 16

So one number is 16 and other number is 20 – 16, i.e. 4.

Using method 2 (Double Variable):Suppose the numbers are ‘x’ and ‘y’

According to the first given condition,

Sum of two number is 20.

x + y = 20 …(i)

According to second given condition,

Difference of two number is 12.

x – y = 12 …(ii)

On adding equation (i) and (ii),

x + y + x – y = 20 + 12

2x = 32

x = 36/2

x = 16

Now putting the value of x in equation (i),

16 + y = 20

y = 20 – 16

y = 4

The two number having sum 20 and difference 12 are 16 and 4.

**Question 2: If the sum of two numbers is 24 and one number is 7 then find the other number.**

**Solution:**

This problem can be solved by using single variable equation because we have only one unknown.

Suppose the other number is ‘x’.

According to question, Sum of two number is 24.

x + 7 = 24

x = 24 – 7

x = 17

So the other number is 17, whose sum with 7 is 24.

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