Answer:
basketball game tickets: $7.25;
football game tickets: $6.50
Step-by-step explanation:
Let B represent the cost of a basketball ticket and F represent the cost of a football ticket.
Amount for basketball ticket plus amount for football tickets equal the total cost.
4B + 5F = 61.50
5B + 3F = 55.75
Choose one equation in the system to solve for a variable.
Solve the first equation for F.
4B + 5F = 61.50
5F = −4B + 61.50 Subtract 4B from both sides.
F = −0.8B + 12.30 Divide both sides by 5.
Substitute the expression −0.8B + 12.30 for F in the other equation.
5B + 3F = 55.75
5B + 3(−0.8B + 12.30) = 55.75 Substitute.
5B − 2.4B + 36.90 = 55.75 Distribute.
2.6B + 36.90 = 55.75 Combine like terms.
2.6B = 18.85 Subtract 36.90 from both sides.
B = 7.25 Divide both sides by 2.6.
Substitute the B-value into one of the original equations to solve for F.
4B + 5F = 61.50
4(7.25) + 5F = 61.50 Substitute.
29 + 5F = 61.50 Multiply.
5F = 32.50 Subtract 29 from both sides.
F = 6.50 Divide both sides by 5.
The cost of a basketball ticket is $7.25, and the cost of a football ticket is $6.50.
The cost of basketball game tickets is $7.15 and football game ticket is $6.5
Let the cost of a basketball game ticket be x
Let the cost of football game ticket be y
If 4 basketball game tickets and 5 football game tickets were purchased for $61.50, hence;
4x + 5y = 61.50 ..................1
If 5 basketball game tickets and 3 football game tickets were purchased for $55.75, hence;
5x + 3y = 55.75 ...........................2
Solving 1 and 2 simultaneously
4x + 5y = 61.50 ..................1 * 3
5x + 3y = 55.75 ...........................2 * 5
_________________________________
12x + 15y = 184.5
25x + 15y = 278.75
Subtract
12x - 25x = 184.5 - 278.75
-13x = -94.25
x = 7.25
Substitute x = 7.25 into equation 1:
From 1:
4x + 5y = 61.50
4(7.25) + 5y = 61.50
29 + 5y = 61.50
5y = 61.50 -29
5y = 32.5
y = 32,5/5
y = 6.5
Hence the cost of basketball game tickets is $7.15 and football game ticket is $6.5
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