# chole is buying souvenirs on vacation. she wants to spend $70 at most but only has 60 cubic inches of space available in her lugage. if bracelets cost $7 and take up 3 inches of space and t-shirts...

chole is buying souvenirs on vacation. she wants to spend $70 at most but only has 60 cubic inches of space available in her lugage. if bracelets cost $7 and take up 3 inches of space and t-shirts are $5 but take 15 inches of space, write and graph a system of four inequalites that model chloe's possible purchases. letx=number of bracelets and y=number of t-shirts; use a scale of 2 on both axes.

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### 1 Answer

x = number of bracelets

y = number of t-shirts

1) For non-negative number of bracelets: `x gt= 0 `

2) For non-negative number of t-shirts: `y gt= 0 `

3) The total amount Chloe spends will be the number of bracelets purchased (x) times 7, plus the number of t-shirts (y) times 5. The total spent must be less than or equal to 70. So,

`7x + 5y lt= 70 `

4) The total amount of space used will be the number of bracelets (x) times 3 cu inches each, plus the number of t-shirts (y) times 15 cu inches. The total amount of space must be less than or equal to 60 cu inches.

`3x + 15y lt= 60 `

The graph:

The small quadrilateral formed by the sides of the both lines towards (0,0) in the bottom left corner in the first quadrant is the feasible region or the solution set.

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