Rick is buying souvenirs on vacation. He wants to spend $70 at most, but only has 60 cubic inches of space available in his suitcase.  If braclets cost $7 and take up 3 cubic in. of space and...

Rick is buying souvenirs on vacation. He wants to spend $70 at most, but only has 60 cubic inches of space available in his suitcase.  If braclets cost $7 and take up 3 cubic in. of space and t-shirts are $5 but take 15 cubic in. of space, write and graph a system of FOUR inequalities that model Rick's possible purchases.  Let x = number of braclets and y= number of t-shirts.

Please show steps and also please show on graph. The graph needs to have a scale of 2 on both axes.

Thanks!

Asked on by marley112

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baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

If x = number of bracelets and y = the number of t-shirts, then 7x and 5y respectively represents the cost of each, and 3x and 15y represents total space respectively.

Therefore, the 4 equations are:

`x>=0`

`y>=0`

`7x + 5y<= 70`

`3x+15y <= 60`

Graphs shown in attachment.  The intersection of all four is the darkest shaded portion just above the x-axis and to the right of the y-axis.

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