Question

The sum of two numbers is 46 and the difference is 14. What are the numbers?

Answer 1

Let x represent the larger number.
.. x -(46 -x) = 14 . .the difference is 14
.. 2x = 60 . . . . . . simplify
.. x = 30 . . . . . . . divide by 2
The larger number is 30; the smaller is 16.

Answer 2

X is the larger of the two numbers.
x + y = 46
x - y = 14 Add these two equations.
2x = 60 Divide by 2.
x = 60/2
x = 30
x + y =  46 Put 30 in for x
30 + y = 46 Subtract 30
y = 36 - 30
y = 16

the larger number is 30. The smaller is 16