SOLUTION: Cesar sells his drawings at the county fair. He wants to sell at least 6 drawings and has portraits and landscapes. He sells the portraits for $24 and the landscapes for $9. He nee

Question 1205787: Cesar sells his drawings at the county fair. He wants to sell at least 6 drawings and has portraits and landscapes. He sells the portraits for $24 and the landscapes for $9. He needs to sell at least $72 worth of drawings in order to earn a profit.
Graph the system on your own graph paper with portraits as the independent variable and landscapes as the dependent variable. Then, decide which of the four graphs below shows the correct lines (dotted/solid), and then choose the letter for the region on that graph that should be shaded for the solution. If no regions should be shaded, choose No Solution.
A B C D E F G H I J K L M N O P No Solution
Will he make a profit if he sells 1 portrait and 7 landscapes?
Will he make a profit if he sells 5 portraits and 4 landscapes?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
here's the graph.]

any point on that line and to the right and above it is valid.

for example:

the point (0,8) is valid because 0 * 24 + 8 * 9 = 72 which is >= 72.

the point (2,2) is not valid because 2 * 24 + 2 * 9 = 66 which is not >= 72.

you can look at the points that are on your graph and determine very quickly whether they are valid based on whether they are on the line or to the right and above the line.

you can also evaluate each point by replacing the x value of that point and the y value of that point with the values of x and y obtained from the equation at that point and determine whether the value of y is greater than or equal to 72.

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