The sum of two numbers is 102. The difference of the same two numbers is 40. Find the two numbers.

Question

The sum of two numbers is 102. The difference of the same two numbers is 40. Find the two numbers.

Answer 1

using algebra...

x+y=102

x-y=40

add

2x=142

x=142/2

x=71

71+y=102

y=102-71

y=31

71 and 31 are the numbers

using arithmetic...

102/2=51

51+20=71

51-20=31

 

Answer 2

Hi Loppy,

 

The sum of two numbers is 102. The difference of the same two numbers is 40. Find the two numbers.

 

Let x=1st number

Let y= 2nd number

 

x+y=102

x-y=40

 

This system can be solved by Elimination

 

x+y=102
x-y=40

---------

2x=142

x=71

 

Substitute the x-value into the 1st equation

x+y=102

71+y=102

y=31

 

ANSWER:  The two numbers are 71 and 31.