Question

Jane and Beth are selling cookies and cakes to make money they sell the cookies for $3 each and the cakes for $12 each in order for Jane and best to make at least $300 what is the minimum number of cakes they must sell if they only sell 25 cookies

Answer 1

We can write the sales amount as the sum of the sales of the cookies and the sales of the cakes. Each one of these is the price times the quantity of each item.

Let X be the amount of cookies and Y be the amount of cakes.

Then, the total sales S will be:

`S=3\cdot X+12\cdot Y`

If we know the must sell 25 cookies (X=25) and the total sales are at least $300 (S>=300), we can calculate the amount of cakes they need to sell as:

`\begin{gathered} S\ge300 \\ 3\cdot25+12Y\ge300 \\ 75+12Y\ge300 \\ 12Y\ge300-75 \\ 12Y\ge225 \\ Y\ge(225)/(12) \\ Y\ge18.75 \end{gathered}`

They have to sell at least 19 cakes (rounding 18.75 to the next integer that satisfy the inequality) to make $300 in sales.

Answer: the minimum number of cakes is 19.