What would the inequalities be and how do you determine them?

Question

Mom is buying gifts while on vacation. She wants to spend $70 at most, but only has 60 cubic inches in her luggage available. If necklaces cost $7 and take up 3 cubic inches of space and hats are $5 but take up 15 cubic inches of space, write and graph a system of 4 inequalities that model Mom's possible choices. Let x= number of necklaces and y = number of hats.

What would the inequalities be and how do you determine them?

Answer 1

Hi Allison

 

Let's set this up

 

x = # necklaces

They cost $7 each and take up 3 cubic inches

y = #hats

They cost $5 each but take up 15 cubic inches

 

She wants to spend no more than $70, i.e. ≤ 70

She has only 60 cubic inches of space, i.e. ≤ 60

 

Let's set up an inequality for the cost

7x + 5y ≤ 70

 

And the inequality for the space

3x + 15y ≤ 60

 

We have a system of two inequalities and two unknowns which we can graph

7x + 5y ≤ 70

3x + 15y ≤ 60

 

But first it helps to put them in slope intercept form

y ≤ (-7/5)x + 14

y ≤ (-1/5)x + 4

 

Graph each inequality and shade the area below the line since y is less than the expression.

The area of overlapping shading contains the various combinations of choices.