If 4 basketball game tickets and 5 football game tickets were purchased for $61.50, and if 5 basketball game tickets and 3 football game tickets were purchased for $55.75, what are the costs of basketball game tickets and football game tickets?

Answers

Answer 1

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.

Answer 2

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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