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

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

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!