$100 for 100 pens

Your boss has asked you to purchase three different types of ballpoint pen. The first costs 50, the second $5.50, and the third $9.50. He has given you $100 and told you to purchase 100 pens in any combination as long as you spend exactly $100 for 100 pens. Just one solution is possible. Can you find it?

Hint: Familiarity with solving simultaneous equations would be helpful here.

Answer:

It is always helpful to set up a legend of what is given and to work from there.

X = $.50 pens
Y = $5.50 pens
Z = $9.50 pens

Set up two equations as follows:

X + Y + Z = 100
$.50X + $5.50Y + $9.50Z = 100

Now, we need at least one of the values to drop out in order to consider the other two. Multiply the first equation by - .5 to drop X out of both equations.

- 0.5X - 0.5Y - 0.5Z = -50
+ 0.5X + 5.5Y + 9.5Z = 100
__________________________
+ 5.0Y + 9.0Z = 50

5Y = 50 - 9Z
Y = 10 - Z

Since we're dealing with whole numbers, Z must be a whole number and a multiple of 5. In this case, Z can only equal 5. With any greater number, Y will become a negative number. So, Z = 5 and Y becomes 1 leaving X to be 94 pens at $.50.

94 pens at $.50
1 pen at $5.50
5 pens at $9.50