Part A)
The jazz band sells 31 large boxes of fruit and 74 small boxes of fruit.
For each large fruit box, the price is $20 and cost is $x.
Profit is defined as Price - Cost.
So, profit for one large fruit box = 20 - x
Profit for 31 large fruit boxes = 31(20 - x)
Price of each small fruit box is $10 and cost of each small fruit box is $y. The profit for each small fruit box is 10 - y.
Profit for 74 small fruit boxes = 74(10 - y)
The total profit for 31 large boxes and 74 small boxes will be:
Total profit = 31 (20 - x ) + 74(10 - y)
Using distributive property, we can simplify the above equation as:
Total profit = 31(20) - 31x +74(10) - 74y
Total profit = 1360 - 31x - 74y
Part B)
Cost of each large box is given to be $9. This means x = 9
Cost of each small box is given to be $4. This means y = 4
Using the values of x and y in the profit equation we can find the profit of the Jazz Band.
So, Jazz Band's Profit = 1360 - 31(9) - 74(4)
Jazz Band's Profit = $ 785
Thus the profit of Jazz Band will be $785.
