To determine how many newspapers were sold at \[tex]$0.25, let’s follow a step-by-step approach:
1. Define Variables:
- Let \( x \) be the number of newspapers sold at \$[/tex]0.25 each.
- Since the total number of newspapers sold is 100, the number of newspapers sold at \[tex]$0.40 each would be \( 100 - x \).
2. Set Up the Equation:
- The total revenue from the newspapers sold at \$[/tex]0.25 each is [tex]\( 0.25x \)[/tex] dollars.
- The total revenue from the newspapers sold at \[tex]$0.40 each is \( 0.40(100 - x) \) dollars.
- The total revenue from selling 100 newspapers is \$[/tex]28.00.
3. Formulate the Equation:
- The total revenue equation is:
[tex]\[
0.25x + 0.40(100 - x) = 28.00
\][/tex]
4. Simplify the Equation:
- Distribute the 0.40 in the second term:
[tex]\[
0.25x + 40 - 0.40x = 28.00
\][/tex]
- Combine like terms (0.25x and -0.40x):
[tex]\[
0.25x - 0.40x + 40 = 28.00
\][/tex]
[tex]\[
-0.15x + 40 = 28.00
\][/tex]
5. Solve for [tex]\( x \)[/tex]:
- Subtract 40 from both sides of the equation:
[tex]\[
-0.15x = 28.00 - 40
\][/tex]
[tex]\[
-0.15x = -12.00
\][/tex]
- Divide both sides by -0.15:
[tex]\[
x = \frac{-12.00}{-0.15}
\][/tex]
[tex]\[
x = 80
\][/tex]
Therefore, the vendor sold [tex]\( \boxed{80} \)[/tex] newspapers at \$0.25 each.
