Question

The second of two numbers is 3 less than twice the first. Their sum is 36. How do you find the numbers?

Answer 1

The second number would be 23, the first would be 13.

Explanation:

Using the clues given, we can determine that 2 equations are true:
For this we will assume that `a` = first number and `b` = second number.

`b = 2a - 3`
The second number is 3 less than 2 times the first
`a+b=36`
The sum of the numbers is 36.

We can then manipulate either equation to substitute in a variable, since `b` is already set equal to something, we will use that as our substitute.

`a + (2a-3) = 36`
`3a - 3 = 36`
`3a = 39`
`a = 13`

Now that we have the first number, we can plug that value in for `a` in either of the two equations, let's use the one set equal to `b`.

`b = 2(13) - 3`
`b = 26 - 3`
`b = 23`

This gets us our two numbers, if needed, we can check by looking at the clues again and seeing if they fit, which they do.

Hope this helped!

Answer 2

Find 2 numbers

Explanation:

Call x the first number and y the second one.
We have two equations:
x + y = 36 (1)
y = 2x - 3 (2)
From (1) --> y = 36 - x. Substitute this value into (2):
36 - x = 2x - 3
3x = 39
x = 13 --> y = 36 - 13 = 23.

Check: y = 2(13) - 3 = 23. OK