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.

Question - how many of each type of football did they order? (solve using elimination)

X = Footballs sold @ $22 ea.

Y = Footballs sold @ $6 ea.

Eq1: x + y = 6000
Eq2: 22x + 6y = $76,000
Multiply Eq1 by -6 and add the Eqs:
-6x - 6y = -36000
22x + 6y = 76,000
Sum: 16x = 40,000
X = 2500

In Eq1, replace X with 2500:
2500 + y = 6000
Y = 6000-2500 = 3500

Let's solve this problem using the elimination method.

Let's assume they ordered x number of original full-size logo footballs.
So, the number of miniature logo footballs ordered would be 6000 - x.

The cost of each original full-size logo football is $22, and the cost of each miniature logo football is $6.
Therefore, the total revenue from selling the original full-size logo footballs would be 22x dollars, and the total revenue from selling the miniature logo footballs would be 6(6000 - x) dollars.

According to the problem, the total revenue from selling all 6000 footballs is $76000.
So, we can set up the equation:

22x + 6(6000 - x) = 76000

Now, let's solve this equation step by step:

22x + 36000 - 6x = 76000
16x + 36000 = 76000
16x = 40000
x = 2500

Therefore, they ordered 2500 original full-size logo footballs and 6000 - 2500 = 3500 miniature logo footballs.

To solve the problem using the elimination method, we need to set up a system of equations. Let's represent the number of full-size logo footballs as x and the number of miniature logo footballs as y.

The given information tells us the following:
1) The price of a full-size logo football is $22, and the price of a miniature logo football is $6.
2) They ordered a total of 6000 footballs.
3) The total amount made by selling all the footballs is $76000.

Based on this, we can create two equations:

Equation 1: x + y = 6000 (since the total number ordered is 6000)
Equation 2: 22x + 6y = 76000 (since the total amount made is $76000)

Now, we can solve this system of equations using the elimination method.

To eliminate the variable y, we will multiply Equation 1 by 6 and Equation 2 by -1, and then add the resulting equations together:

6(x + y) = 6(6000)
-1(22x + 6y) = -1(76000)

This simplifies to:
6x + 6y = 36000
-22x - 6y = -76000

Adding these equations gives:
6x - 22x + 6y - 6y = 36000 - 76000
-16x = -40000
Dividing both sides by -16:
x = 2500

Now that we have the value of x, we can substitute it into Equation 1 to find y:

2500 + y = 6000
y = 6000 - 2500
y = 3500

Therefore, they ordered 2500 full-size logo footballs and 3500 miniature logo footballs.