Mary's children decide to run a lemonade stand to earn some extra money. the cost to start the buisness is $1.20 and each cup of lemonade costs 6 cents to make. if lemonade sells for 10 cents a cup, how many cups must mary's children sell to make a profit?

The correct answer is more than 30 cups.

Step-by-step explanation:

Step 1:

Determine the cost function for this business.

The fixed costs for this business is $1.20. The variable costs for this business is where is the number of cups of lemonade created.

The cost function for this business is the sum of the fixed costs and the variable costs. For this businesses the cost function is,

Step 2;

The next step is to determine the revenue function for this business.

Since every unit sells for $0.10, the revenue function for this business is,

Step 3

The next step is to realize that the business will make a profit after it's break even point, i.e the point at which the revenue from the business is equal t the cost of operating the business. The break even point is calculated as show blow,

The break even point occurs at 30 cups of lemonade sold. To makes a profit, the stall has to sell more than 30 cups.

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

4 candies

step-by-step explanation:

7 x 28 = 196

200 - 196 = 4 candies remaining.