Sum of two numbers is 17 and their difference is 7. Find the numbers

The sum of two number is 17 and their difference is 7 then the two numbers are either 12 and 5 or 10 and 40.

Let us suppose the numbers are x and y then,

The sum of the two numbers is 17 i.e.,

x + y = 17 . . .(i)

The difference between the two numbers is 30 i.e.,

∣x−y∣ = 7 . . . (ii)

From equation i, we can express y in terms of x we get,

y = 17 − x

Putting this value Substituting this expression for y into another equation , we get,

∣x − (17−x)∣ = 7

∣x − 17 + x∣ = 7

∣2x − 17∣ = 7

2x − 17 = ±7

2x = 17 ±7

⇒ x = 12 or x = 5.

For x = 12 we get y = 5 and for x = 5 we get y = 12.

This equation has two possible solution. The two numbers are either 12 and 5, or 5 and 12.

What is Linear Equation?

Linear equations in one variable are equations that are written as ax + b = 0, where a and b are two integers and x is a variable, and there is only one solution. 3x+ 2 = 5, for example, is a linear equation with only one variable. As a result, there is only one solution to this equation, which is x = 1. A linear equation in two variables, on the other hand, has two solutions.

A one-variable linear equation is one with a maximum of one variable of order one. The formula is ax + b = 0, using x as the variable.

There is just one solution to this equation. Here are a few examples:

• 4x = 8
• 5x + 10 = -20
• 1 + 6x = 11

Linear equations in one variable are written in standard form as:

ax + b = 0

Here,

• The numbers ‘a’ and ‘b’ are real.
• Neither ‘a’ nor ‘b’ are equal to zero.

Similar Questions

Question 1: The sum of two numbers is 20, and the difference between the two numbers is 10. The task is to find the numbers.

Solution:

Let both numbers be first and second.

According to the problem statement:
first + second = 20 (Consider this as 1st equation)
first – second = 10  (Consider this as 2nd equation)

Add both equations:

first + second + first – second = 20 + 10
2 * first = 30
first = 30 / 2
first = 15

So from this we get first = 15, put this value in any equation i.e.

first + second = 20 (Put the value of first in this equation)
15 + second = 20
second = 20 – 15
second = 5

So, the numbers are 15 and 5.

If we consider the case i.e. second – first = 10 then the solution will be same and the first number will become 5 and second number will become 15.

Question 2: What two numbers have a sum of 9 and a difference of 5?

Solution:

Let both numbers be first and second.

According to the problem statement:
first + second = 9 (Consider this as 1st equation)
first – second = 5  (Consider this as 2nd equation)

Add both equations:

first + second + first – second = 9 + 5
2 * first = 14
first = 14 / 2
first = 7

So from this we get first = 7, put this value in any equation i.e.

first + second = 9 (Put the value of first in this equation)
7 + second = 9
second = 9 – 7
second = 2

So, the numbers are 7 and 2.

If we consider the case i.e. second – first = 5, then the solution will be same and the first number will become 2 and second number will become 7.