# What are the two numbers that are the sum 50 difference 10 ? thank you

##### 3 Answers

#### Answer:

See below.

#### Explanation:

Firstly, assign the two numbers random variables

The sum of them is equal to

The difference is

Now we have a simultaneous equation.

Add them together to cancel out the

Now solve for

Now put the value back into one of the equations to find

The two numbers are

#### Answer:

#### Explanation:

#"let the 2 numbers be x and y ";x>y#

#x+y=50larrcolor(blue)"sum of numbers"#

#x-y=10larrcolor(blue)"difference of numbers"#

#"add the 2 equations term by term on both sides"#

#(x+x)+(y-y)=(50+10)#

#2x=60#

#"divide both sides by 2"#

#x=60/2=30rArrx=30#

#"substitute " x=30" into "x+y=50#

#30+y=50#

#"subtract 30 from both sides"#

#y=50-30=20rArry=20#

#"the 2 numbers are 30 and 20"#

#### Answer:

30 and 20

#### Explanation:

Okay let's define a couple numbers, let's call one of them

We are told that the sum (addition) is:

And the difference (subtraction):

We have a system of equations; two equations and two unknown variables so it is solvable; we will use the "substitution" method:

add

now substitute the value we solved for

So one of the numbers is

Solved! Our numbers are 30 and 20

To check your solutions insert them into the original equations:

and