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We are buying glazed and chocolate donuts.  The glazed donuts cost .15 each and...

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mpumpkin | (Level 1) Valedictorian

Posted June 1, 2013 at 11:39 PM via web

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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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crmhaske | College Teacher | (Level 3) Associate Educator

Posted June 2, 2013 at 12:24 AM (Answer #1)

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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

Sources:

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