A school choir needs to make T-shirts for its 75 members and has set aside some money in their budget to pay for them. The members of the choir decided to order from a printing company that charges $3 per shirt, plus a $50 fee for each color to be printed on the shirts. Write an equation that represents the relationship between the number of T-shirts ordered, the number of colors on the shirts, and the total cost of the order. If you use a variable, specify what it represents. In this situation, which quantities do you think can vary? Which might be fixed?

The equation = 50 + 3 (B) + 50 + 3 (R) + 50 + 3 (Y)

The variable quantities are the number of members that each colour will be printed for and the cost of printing a shirt.

The fixed quantity is the charge for each colour that will be printed.

Step-by-step explanation:

Let us assume that the members of the choir chose three colours. The colours chosen are: - Blue, red and yellow. Out of the 75 members of the choir, some chose blue colour, some went for red colour and the remainder settled for yellow colour.

Let us use "B" to denote the number of choir members that went for blue colour, R for the number of choir members that opted for red T-shirts and Y for those that chose yellow. The expression that we have now is:

B + R + Y = 75

Since the printing company charges a $50 fee for each colour to be printed on the shirts and $3 per shirt printed, then the cost for printing blue shirts for the members of the choir that chose blue = 50 + 3 (B).

The cost for printing red shirts for the choir members that preferred red = 50 + 3R and the cost of printing yellow T-shirts for those opted for this colour = 50 + 3 (Y).

The total cost of printing shirts for all members of the choir will now be:

50 + 3 (B) + 50 + 3 (R) + 50 + 3 (Y)

This is the equation that can be used to calculate the total cost of printing shirts for all members of the choir.

Now, let us assume that 36 members chose blue colour, 14 members went for red and 25 yellow yellow T-shirts were printed for those that went for them. The total cost of printing the shirts will now be:-

50+3 (36) + 50+3 (14) + 50+3 (25)

50+108 + 50+42 + 50+75

158 + 92 + 125 = $375

From this solved example, we can see that the quantities that are varying are the number of choir members that chose each colour as well as the cost for printing the shirts for the varying number of members that chose each colour.

The only fixed quantity here is the charge for each colour printed. This quantity does not depend on the number of members that the colour will be printed for like the $3 per shirt printing cost.