The Eskimos are trying to generate more money because player wages are increasing. they have came up with a couple of plans:
Plan 1 : they are going to open up 1850 new seats in the endzone that will be reserved for family seating. they project that they will, on average, get 1850 adults and children to fill those seats if they charge $4.50 per child and $7.50 per adult and they should make $10125.00
a)how many adults and children are needed per game (solve using substitution)
b)how many money do they generate over the course of a 16 game season?
Plan 2: they are planning to sell 75 year anniversary logo football to help raise money. an original full size logo football will sell for $22 and a miniature logo football will sell for $6. if they sell all 6000 footballs they ordered they can make $76000.
c) how many of each type of football did they order?(solve using elimination)
a) To solve using substitution, we need to set up a system of equations based on the information given. Let's assume the number of children attending the game is represented by 'c' and the number of adults attending is represented by 'a'.
From the problem statement, we know that the total number of people attending the game is 1850. This can be expressed as:
c + a = 1850 -- (Equation 1)
We are also given the ticket prices. The total revenue from the family seating section is projected to be $10125. This can be expressed as:
4.50c + 7.50a = 10125 -- (Equation 2)
To solve using substitution, we can isolate one variable from Equation 1 and substitute it into Equation 2.
If we isolate 'c' from Equation 1, we get:
c = 1850 - a
Substituting this value of 'c' into Equation 2, we get:
4.50(1850 - a) + 7.50a = 10125
Now, we can solve this equation to find the value of 'a' (number of adults).
4.50(1850) - 4.50a + 7.50a = 10125
8325 + 3a = 10125
3a = 1800
a = 600
Now that we have the value of 'a', we can substitute it back into Equation 1 to find the value of 'c':
c + 600 = 1850
c = 1250
Therefore, the Eskimos would need 600 adults and 1250 children to fill the 1850 new seats in the endzone for each game.
b) Now that we know the number of adults (600) and children (1250) attending each game, we can calculate the total revenue generated for each game using the given ticket prices:
Total revenue per game = (Number of children * Child ticket price) + (Number of adults * Adult ticket price)
= (1250 * $4.50) + (600 * $7.50)
= $5625 + $4500
= $10125
Since this revenue is projected to be generated for each of the 16 games in a season, we can calculate the total revenue generated over the course of the season:
Total revenue over 16 games = Total revenue per game * Number of games
= $10125 * 16
= $162,000
Therefore, the Eskimos would generate $162,000 over the course of a 16-game season.
c) To solve using elimination, let's assume the number of full-size logo footballs ordered is 'f' and the number of miniature logo footballs ordered is 'm'.
From the problem statement, we know that the total number of footballs ordered is given as 6000. This can be expressed as:
f + m = 6000 -- (Equation 3)
We are also given the prices for each type of football and the total revenue projected to be $76000. This can be expressed as:
22f + 6m = 76000 -- (Equation 4)
To solve using elimination, we can multiply Equation 3 by 6 and Equation 4 by -1 to eliminate the variable 'm'.
6f + 6m = 36000
-22f - 6m = -76000
Adding these two equations together, we get:
-16f = -40000
f = 2500
Substituting the value of 'f' back into Equation 3, we can solve for 'm':
2500 + m = 6000
m = 3500
Therefore, the Eskimos ordered 2500 full-size logo footballs and 3500 miniature logo footballs.