Word Problem

Question

A person wants to purchase two types of items, A and B, from a shop. She has $200 to spend and she has to purchase at least 10 items. if the purchase price of one unit of each A and B is $10 and $30 respectively, represent this problem graphically.

Answer 1

Let x be the number of items of item A

Let y be the number of items of item B

 

You automatically have the equations x>=0 and y>=0 (since you can't purchase a negative number of items)

 

Since she has to purchase at least 10 items you get the equation

x + y >= 10

 

Since she only has $200 to spend you get the equation

10x +30y <= 200

 

Now manipulating the equations above you have the following 4 equations:

x>=0

y>=0

y>= -x +10

y<= -(1/3)x + (20/3)

 

Graph each of these lines.  Shade above the x axis, shade to the right of the y axis. For the 3rd line shade above the line, and for the 4th line shade below it.  The intersection of all the shading is your solution.