# We are buying glazed and chocolate donuts. The glazed donuts cost .15 each and chocolate cost .25 each. we want to buy a mixture of both of at least 48 donuts and spend less than 12. Set up...

We are buying glazed and chocolate donuts. The glazed donuts cost .15 each and chocolate cost .25 each. we want to buy a mixture of both of at least 48 donuts and spend less than 12.

Set up the system of linear inequalities and solve:

We know that g+c is great than or equal to 48

.15g+.25c is less than 12.00

We keep coming up with something that does not work base on the question

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Let g = number of glazed donuts

Let c = number of chocolate donuts

`g+cgt=48`

`ggt=48-c`

`0.15g+0.25clt12`

`0.15glt12-0.25c`

`glt80-5/3c`

So, now we have two constraints for g. We also know that g>0 and c>0, since you cannot buy negative donuts.

`ggt=48-c`

`glt80-5/3c`

Graph them:

The region between the black (g=48-c) and red lines (g=80-(5/3)c) bounded by the lines g=0 and c=0 are the solutions to the inequalities. Therefore (approximately):

0<c<48 and 0<g<80