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 tennis league and an Independent basketball league totaled $123.62. The basketball FCI was $$6.98 more than that of tennis. What were the FCIs for these sports ? The FCI for tennis was$_____ and the FCI for basketball was $_____.
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Let's represent the FCI for tennis as "x" dollars.
According to the given information, the FCI for basketball is $6.98 more than that of tennis. So, the FCI for basketball can be represented as "x + $6.98".
The total FCI for both sports is $123.62.
Therefore, we can set up the equation:
x + (x + $6.98) = $123.62
Simplifying the equation:
2x + $6.98 = $123.62
2x = $123.62 - $6.98
2x = $116.64
x = $116.64/2
x = $58.32
So, the FCI for tennis is $58.32 and the FCI for basketball is $58.32 + $6.98 = $65.30.
To solve this problem, we can set up a system of equations based on the given information. Let's use the variable 't' to represent the cost of the tennis FCI and 'b' to represent the cost of the basketball FCI.
From the information given, we can establish the following equations:
Equation 1: t + b = 123.62 (the FCIs for tennis and basketball totaled $123.62)
Equation 2: b = t + 6.98 (the basketball FCI was $6.98 more than the tennis FCI)
To find the values of 't' and 'b', we can use a method called substitution. We'll solve Equation 2 for 't' and substitute it into Equation 1:
Substituting Equation 2 into Equation 1, we get:
(t + 6.98) + t = 123.62
Combining like terms:
2t + 6.98 = 123.62
Subtracting 6.98 from both sides:
2t = 116.64
Dividing both sides by 2:
t = 58.32
Now that we know the value of 't', we can substitute it back into Equation 2 to find 'b':
b = 58.32 + 6.98
b = 65.30
Therefore, the FCI for tennis is $58.32 and the FCI for basketball is $65.30.
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