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

3 Answers
May 25, 2018

Answer:

See below.

Explanation:

Firstly, assign the two numbers random variables #x# and #y#

The sum of them is equal to #50# therefore

#x+y=50#

The difference is #10#

#x-y=10#

Now we have a simultaneous equation.
#x+y=50#
#x-y=10#

Add them together to cancel out the #y#.

#2x=60#

Now solve for #x# #=> x=30#

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

#y+30=50#
#=> y=20#

The two numbers are #30# and #20#

May 25, 2018

Answer:

#30" and "20#

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"#

May 25, 2018

Answer:

30 and 20

Explanation:

Okay let's define a couple numbers, let's call one of them #x# and the other #y#.

We are told that the sum (addition) is:

#x+y =50#

And the difference (subtraction):

#x-y=10#

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

add #y# to both sides of: #x-y=10#

#x-y +y=10+y#

#x=10+y#

now substitute the value we solved for #x# into the other equation:

#x+y =50#

#(10+y)+y =50#

#10+2y =50#

#2y =40#

#y=20#

So one of the numbers is #20#. to find the other use either of our original equations and insert #y# to solve for #x#, this one is simplest:

#x+y =50#

#x+20 =50#

#x =30#

Solved! Our numbers are 30 and 20

To check your solutions insert them into the original equations:

#x+y =50#

#30+20 =50#

and

#x-y=10#

#30-20=10#