a. Since the iced tea is sold for $0.50 per cup and the lemonade is sold for $0.80 per cup, the equation can be written as:
0.50x + 0.80y = 240.00
b. The x intercept is (480, 0) and the y intercept is (0, 300). These intercepts represent the number of cups of each beverage needed to cover the costs.
a. To find out how many cups of each beverage must be sold to raise $240.00, we can set up an equation using the given information. Let's say x represents the number of cups of iced tea sold and y represents the number of cups of lemonade sold.
Since the iced tea is sold for $0.50 per cup and the lemonade is sold for $0.80 per cup, the equation can be written as:
0.50x + 0.80y = 240.00
b. To find the x and y intercepts of the equation, we can set one variable to zero and solve for the other variable.
To find the x intercept, we set y = 0 and solve for x:
0.50x + 0.80(0) = 240.00
0.50x = 240.00
x = 480
So the x intercept is (480, 0), which means that 480 cups of iced tea need to be sold to cover the costs without selling any cups of lemonade.
To find the y intercept, we set x = 0 and solve for y:
0.50(0) + 0.80y = 240.00
0.80y = 240.00
y = 300
So the y intercept is (0, 300), which means that 300 cups of lemonade need to be sold to cover the costs without selling any cups of iced tea.
Therefore, the x intercept is (480, 0) and the y intercept is (0, 300). These intercepts represent the number of cups of each beverage needed to cover the costs.