Question

one number exceeds another by 20. The sum of the number is 66. What are the numbers?

Answer 1

let the numbers be A and B, so say A exceeds B by 20.

Then instead of saying "A", you could say "B+20" Would you agree?

Answer 2

Since we don't know the numbers let x and y be the numbers with x > y.

Answer 3

So, the sum of A and B is 60....... 60 = A + B
But you can call "A" as "B+20" so 60 = (B+20) + B

Answer 4

oops, meant to write 66, not 60

Answer 5

Then since x > y, it implies x - y = 20

Answer 6

66 = (b+20) + b
66 = 2b + 20
46 = 2b
b = 23

a = b+20, so a = 23+20 = 43

The two numbers are 43 and 23 (Check: 23 + 43 = 66)

Answer 7

Also x + y = 66
This gives us two equations in two variables
Hence, solve x - y = 20 and x + y = 66 simultaneously

Answer 8

If this is early algebra, they may not be at 2 variable problems yet. Often they seem to teach just direct substitution based on the relationship without showing the rigor of the system of 2 equations.

But I wish they'd teach it the way you are :)

Answer 9

You can also use the one variable state approach

Answer 10

Thanks JakeV8 for the appreciation.