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A jazz band sells 31 large boxes of fruit and 74 small boxes of fruit for a fundraiser.

AWrite and simplify an equation using distributive property to find the profit.

BA large box of fruit costs $9 and a small box of fruit costs $4. What is the Jazz's band profit?

Profit = Price - Cost

Large Fruit Box:

Price $20

Cost $x

Small Fruit Box

Price $10

Cost $y

Verified Answer :

a.2(x+2y)=t      b.2(9+(4)2)=t ------> 2(9+8)=t -----> 18+16=t ------> 34=t

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.