Answer :
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.
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.
