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Question

Chloe is buying souvenirs on vacation. She wants to spend $70 at most, but only has 60 cubic inches of space available in her luggage. If bracelets cost $7 and take up 3 inch cubed of space and t-shirts are $5 but take 15 inch cubed of space, write and graph a system of four inequalities that model Chloe's possible purchases. Let x= number of bracelets and y= number of t-shirts; use scale of 2 on both axes.

Answer 1

I can't graph it for you, but I can work out the equations...

 

Let t = the number of t-shirts and let b = the number of bracelets.

 

So the total cost would be 7b + 5t.  That has to be no more than 70, so the first inequality is:

 

7b + 5t ≤ 70

 

The total space taken up would be 3b + 15t, and that has to be no more than 60:

 

3b + 15t ≤ 60

 

The other information we have is that she can't buy a negative number of either item.  She can only buy 0 or more of each item.  So that results in two more inequalities:

 

b ≥ 0

t ≥ 0