The sum of two numbers is 40. The second number is 5 less than twice the first number. Let [tex]x[/tex] represent the first number and let [tex]y[/tex] represent the second number. What is the value of the first number?

Use the table to guess and check.

[tex]
\[
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{4}{|c|}{Numbers} \\
\hline
$x$ & $y$ & $x + y = 40$ & $y = 2x - 5$ \\
\hline
15 & 25 & 40 & 25 = 2(15) - 5 \\
\hline
20 & 20 & 40 & 20 = 2(20) - 5 \\
\hline
25 & 15 & 40 & 15 = 2(25) - 5 \\
\hline
30 & 10 & 40 & 10 = 2(30) - 5 \\
\hline
\end{tabular}
\]
[/tex]

Choose the correct value for the first number:

- 15
- 20
- 25
- 30

To solve the problem where the sum of two numbers is 40 and the second number is 5 less than twice the first number, we will use a guess and check method with the numbers provided.

We are given four possible values for the first number, [tex]$ x $[/tex]: 15, 20, 25, and 30. Let's evaluate each one to see which one fits the conditions.

1. First Number [tex]$ x = 15 $[/tex]:

- Calculate the second number using the formula:
[tex]$ y = 2x - 5 $[/tex]
[tex]$ y = 2(15) - 5 = 30 - 5 = 25 $[/tex]
- Check the sum:
[tex]$ x + y = 15 + 25 = 40 $[/tex]

This option satisfies both conditions: the sum is 40, and the second number is 5 less than twice the first number.

Since this calculation satisfies all the conditions of the problem, the first number [tex]$ x $[/tex] is 15. Therefore, the value of the first number is [tex]$ \boxed{15} $[/tex].