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.,
β£xβyβ£ = 7 . . . (ii)
From equation i, we can express y in terms of x we get,
y = 17 β x
Putting this value Substituting this expression for y into another equation , we get,
β£x β (17βx)β£ = 7
β£x β 17 + xβ£ = 7
β£2x β 17β£ = 7
2x β 17 = Β±7
2x = 17 Β±7
β 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 βaβ and βbβ are real.
- Neither βaβ nor βbβ 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 β second = 10 (Consider this as 2nd equation)Add both equations:
first + second + first β second = 20 + 10
2 * first = 30
first = 30 / 2
first = 15So 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 β 15
second = 5So, the numbers are 15 and 5.
If we consider the case i.e. second β 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 β second = 5 (Consider this as 2nd equation)Add both equations:
first + second + first β second = 9 + 5
2 * first = 14
first = 14 / 2
first = 7So 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 β 7
second = 2So, the numbers are 7 and 2.
If we consider the case i.e. second β first = 5, then the solution will be same and the first number will become 2 and second number will become 7.