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. To find the profit, we need to calculate the total revenue from selling the boxes of fruit and subtract the total cost.
Let's start by calculating the revenue. Since there are 31 large boxes of fruit sold at $20 each and 74 small boxes of fruit sold at $10 each, we can express the revenue as:
Revenue = (31 * Price of Large Fruit Box) + (74 * Price of Small Fruit Box)
Using the given prices, the equation simplifies to:
Revenue = (31 * $20) + (74 * $10)
Now, let's calculate the total cost. We know the cost of the large fruit box is denoted by x, and the cost of the small fruit box is denoted by y. The equation for the total cost is:
Cost = (31 * Cost of Large Fruit Box) + (74 * Cost of Small Fruit Box)
Now, let's put this all together to find the profit using the Profit = Revenue - Cost formula:
Profit = Revenue - Cost
Substituting the calculated values, we have:
Profit = [(31 * $20) + (74 * $10)] - [(31 * x) + (74 * y)]
b. Now that we have the equation for profit, we need to substitute the given values to find the actual profit. According to the given information, a large fruit box costs $9 (x = $9) and a small fruit box costs $4 (y = $4). Now, let's substitute these values into the equation:
Profit = [(31 * $20) + (74 * $10)] - [(31 * $9) + (74 * $4)]
Simplifying this equation will give us the actual profit earned by the jazz band.