SOLUTION: The price for each package of paper of type A, including taxes, is $3 and the price for each package of paper of type B, including taxes, is $4. What is the greatest number of pack

Question 771806: The price for each package of paper of type A, including taxes, is $3 and the price for each package of paper of type B, including taxes, is $4. What is the greatest number of packages of paper a person can buy with exactly $65 ?
Answer by josgarithmetic(39613) (Show Source): You can put this solution on YOUR website!
Type A____________$3 per package_________buy a packages
Type B____________$4 per package_________buy b packages

3a+4b=65
Number of packages is a+b

Other Restrictions:
If a=0 then b=65/4=16&1/4 but this must be taken as 16.
If b=0 then a=65/3=21&2/3 but this must be taken as 21.
The needed restrictions to include then are:

and

You should be able to represent these relations onto a two-dimensional cartesian graph and the combination of a and b which you are looking for would be one of the vertices of the region of the resulting two-dimensional figure. Test each vertex point to see which gives the greatest sum of a+b.
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