Does anyone have an idea?
A jazz band sells 31 large boxes of fruit and 74 small boxes of fruit for a fundraiser.
a. Write and simplify an equation using distributive property to find the profit.
b. A 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
(a) P(x,y) = 31(20-x)+74(10-y)
(b) P(9,4) = 31(20-9)+74(10-4)
a. The equation using the distributive property to find the profit can be written as follows:
Profit = (Price of large boxes * Number of large boxes) + (Price of small boxes * Number of small boxes)
Simplifying this equation, we have:
Profit = (9 * 31) + (4 * 74)
b. Using the given prices of the fruit boxes, we can substitute them into the equation to find the Jazz band's profit:
Profit = (9 * 31) + (4 * 74)
Profit = 279 + 296
Profit = $575
Therefore, the Jazz band's profit is $575.
To solve this problem, we can use the equation:
Profit = Revenue - Cost.
a. To write the equation using the distributive property, we need to consider the quantities sold and their respective prices and costs. Let's assign variables to the unknown quantities:
Let x represent the cost of a large box of fruit.
Let y represent the cost of a small box of fruit.
The revenue from selling the large boxes of fruit is given by:
Revenue from large boxes = Number of large boxes * Price of a large box.
The revenue from selling the small boxes of fruit is given by:
Revenue from small boxes = Number of small boxes * Price of a small box.
The total revenue is the sum of the revenue from the large and small boxes:
Total Revenue = Revenue from large boxes + Revenue from small boxes.
Since profit = Total Revenue - Total Cost, we can rewrite the equation using the distributive property:
Profit = (Number of large boxes * Price of a large box) + (Number of small boxes * Price of a small box) - (Number of large boxes * Cost of a large box) - (Number of small boxes * Cost of a small box).
Simplifying this expression using the distributive property:
Profit = Number of large boxes * (Price of a large box - Cost of a large box) + Number of small boxes * (Price of a small box - Cost of a small box).
b. Now that we have the equation, we can substitute the given values for the prices and costs.
According to the given information:
Number of large boxes = 31.
Number of small boxes = 74.
Price of a large box = $9.
Price of a small box = $4.
We also have:
Cost of a large box = x.
Cost of a small box = y.
Substituting these values into the equation:
Profit = 31 * (9 - x) + 74 * (4 - y).
Now we can solve this equation to find the profit once we have the values of x and y.