Question

The sum of two numbers is 39 and their difference is 5. What is the larger number ?

Answer 1

The numbers are 22 and 17. 22 is the larger number.

22 + 17 = 39
22 - 17 = 5

divided 39 by 2 and its quotient is my basis for addends. Since, 39/2 is 19.50, I rounded it to 20.

20 + 19 = 39 ; 20 - 19 = 1 NO!
21 + 18 = 39 ; 21 - 18 = 3 NO!
22 + 17 = 39 ; 22 - 17 = 5 YES!

Answer 2

sum means add
x+y=39
difference is 5
x-y=5
so we do this
x-y=5
add y to both sides
x=5+y
subsitute 5+y for x
5+y+y=39
add like terms
5+2y=39
subtract 5
2y=34
divide by 2
y=17
subsitute
x=5+y
x=5+17
x=22

the larger number is 22