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

Oct 10, 2015

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.

$b = 2 a - 3$
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.

$a + \left(2 a - 3\right) = 36$
$3 a - 3 = 36$
$3 a = 39$
$a = 13$

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 $b$.

$b = 2 \left(13\right) - 3$
$b = 26 - 3$
$b = 23$

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!

Oct 10, 2015

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