Question

The Fan Cost Index​ (FCI) represents the cost of four​ average-price​ tickets, refreshments, and souvenirs to a sporting event. The FCIs for an independent soccer league and an independent baseball league totaled ​$120.92. The baseball FCI was ​$7.06 more than that of soccer. What were the FCIs for these​ sports?

Answer 1

To find the FCIs for soccer and baseball, we set up a simultaneous equation with the soccer FCI as x and the baseball FCI as x + $7.06. Since their combined total is $120.92, solving for x gives us the soccer FCI of $56.93 and a baseball FCI of $64.99.

Step-by-step explanation:

The question asks to determine the Fan Cost Index (FCI) for both an independent soccer league and an independent baseball league given that the total FCI for both is $120.92 and that the baseball FCI is $7.06 more than the soccer FCI. We can set up two equations to solve this simultaneous equation problem.

Step-by-Step Explanation:

1. Let the FCI for soccer be x dollars.
2. Since the baseball FCI is $7.06 more, its FCI is x + $7.06.
3. The total FCI for both sports combined is $120.92. Therefore, we set up the equation: x + (x + $7.06) = $120.92.
4. Combining like terms gives us: 2x + $7.06 = $120.92.
5. To find x, we subtract $7.06 from both sides: 2x = $120.92 - $7.06, which simplifies to 2x = $113.86.
6. Dividing both sides by 2 gives us the soccer FCI: x = $113.86 / 2, or x = $56.93.
7. Using x, we plug it back into the baseball FCI to find its cost: x + $7.06 = $56.93 + $7.06, which equals $64.99.

Thus, the FCI for the soccer league is $56.93 and for the baseball league, it is $64.99.