The sum of two numbers is 68 and the difference is 10. What are the two numbers?

Question

The sum of two numbers is 68 and the difference is 10. What are the two numbers?

Answer 1

The answers of 29 and 39 are correct.  Algebra was one way to solve.  Other method (not used) was simple number sense.

 

Take away 10 from 68 gives you 58.  Divide 58 by two gives you 29 (the smaller number).  Now add back 10 to 29 gives you 39 (the larger number).  Now add 29 + 39 to get back to 68 (to verify your work).  Since 29 is ten less than 39 you know that you are correct.

Answer 2

Let the first number = x

Let the second number = y

 

 

Set up equations.

 

x + y = 68                 eq1

x - y = 10                  eq2

 

 

We have a system of equations. 

 

Subtract eq2 from eq1 to eliminate the x terms.

 

2y = 58

 

y = 29

 

 

Substitute this value of y into eq1 to solve x.

 

x = 68 - y

x = 68 - 29

x = 39

 

The two numbers are 29 and 39.