Sure, let's solve this step-by-step:
1. Define Variables:
- Let [tex]\( x \)[/tex] be the amount the first person contributed.
- The second person contributed [tex]\( x - 9 \)[/tex] dollars.
- The third person contributed [tex]\( x - 14 \)[/tex] dollars.
2. Formulate the Equation:
- The total cost of the game system is [tex]$298. Therefore, we can set up the following equation reflecting the total contributions of all three friends:
\[
x + (x - 9) + (x - 14) = 298
\]
3. Simplify the Equation:
- Combine the like terms on the left side of the equation:
\[
x + x - 9 + x - 14 = 298
\]
- This simplifies to:
\[
3x - 23 = 298
\]
4. Solve for \( x \):
- Isolate \( 3x \) by adding 23 to both sides of the equation:
\[
3x - 23 + 23 = 298 + 23
\]
- Simplify:
\[
3x = 321
\]
- Divide both sides by 3 to solve for \( x \):
\[
x = \frac{321}{3}
\]
- This results in:
\[
x = 107
\]
5. Find Contributions:
- The first person contributed \( x \), which is $[/tex]107.
- The second person contributed [tex]\( x - 9 \)[/tex]:
[tex]\[
107 - 9 = 98
\][/tex]
- The third person contributed [tex]\( x - 14 \)[/tex]:
[tex]\[
107 - 14 = 93
\][/tex]
6. Conclusion:
- The first person contributed \[tex]$107.
- The second person contributed \$[/tex]98.
- The third person contributed \[tex]$93.
Thus, the contributions of the three friends to the purchase of the game system are \$[/tex]107, \[tex]$98, and \$[/tex]93, respectively.
