Question

Using a System of Inequalities

A pizza parlor charges $1 for each vegetable topping and $2 for each meat topping. You want at least five toppings on your pizza. You have $10 to spend on toppings. How many of each typeof topping can you get on your pizza?

1 x Vegtable Topping + 2 x Meat Topping (less then or equal to) $10
Toppings (greater then or equal to) 5

Is this the correct way to setup the equation and what should I do next? I'm confused because I want to do

X = Number of Vegtable toppings
Y = Number of meat toppings

1x + 2y (less then or equal to) 10

Answer 1

The problem is, the example in my textbook shows a second equation using y, but I'm using y for one of the toppings, not both? So do I follow example or do I need to make a third variable or something?

Answer 2

@Data_LG2 Do you think you can help me out with this one?

Answer 3

your approach is good.

I think you also have to consider this part of the problem " You want at least five toppings on your pizza."

so your second linear inequality
will be \(x+y \ge 5\)

Answer 4

Oh, okay. So then, next would be to make the first equation into slope intercept form.

So,

1x + 2y < 10
-1x
2y < 1x - 10
y < 0.5x (or 1/2x) - 5

Answer 5

yes. that's a good start.