SOLUTION: How do I write and graph an inequality for the following word problem: Suppose you are shopping at the fruit market. You want to spend no ore than $12.00 on apples and bananas. Ban

Question 743223: How do I write and graph an inequality for the following word problem: Suppose you are shopping at the fruit market. You want to spend no ore than $12.00 on apples and bananas. Bananas cost $2.00 per bunch, and apples cost $4.00 per bag.
Answer by davethejackal(28) (Show Source): You can put this solution on YOUR website!
x = number of bags of apples you buy
y = number of bunches of bananas

cost of apples = number of bag x cost per bag ($4) = 4 x
cost of bananas = number of bunches x cost per bunch ($2) = 2 y
Total cost = cost of bananas + cost of apples = 2y + 4x

Total cost must be less than or equal to $12.
Hence
or, if we divide both sides of this inequality by 2 we get

The line y + 2x = 6 defines the boundary. You can draw it by working out where it hits the x and y axes.
When it passes through the y axis, x=0 hence y + 2x = y +0 = 6. Hence the point (0,6) is on the line.
When it passes through the x axis y + 2x = 0 + 2x = 6, this x = 3. Hence the line passes through (3,0)
Draw a line from (3,0) to (0,6) and then pick a random point to the left of the line, e.g. (0,0) at (0,0) y + 2x = 0 + 2(0) = 0 which is less than 6. hence the region to the left of the line is the one which satisfies the inequality, hence shade to the right of the line.

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