Honors algebra question

Question

you receive a gift certificate for a clothing store and plan to use it to buy t shirts and sweatshirts. Describe a situation where you can buy nine t shirts and one sweatshirt but not three shirts and eight sweatshirts. write and graph a system of linear inequalities.

 

PLEASE ANSWER. I NEED AN ANSWER FAST

Answer 1

We want a system of inequalities to graph:

Let t = cost of a tee shirt

Let s = cost of a sweatshirt

Let c = amount of gift certificate

 

9t + s ≤ c

3t + 8s > c

 

If you set an amount for the certificate... say $50.

You can graph the inequalities.  The area in common

will show the cost range for tee shirts and sweatshirts

that fit the scenario.

 

A slightly more realistic set of numbers for an example

would be... tees cost $4 and sweatshirt cost $12 and

we have a $50 gift certificate

 

9t + s ≤ 50

9(4) + 12 ≤ 50

48 ≤ 50

This works.  We can afford 9 tee-shirts and 1 sweatshirt

 

3t + 8s < 50

3(4) + 8(12) < 50

12 + 96 < 50

108 < 50

We cannot afford 3 tee shirts and 8 sweatshirts

Answer 2

You can get as complicated as you like with this.  Since the first is ten items and the second is eleven item, we can make it totally simple by setting price of everything (t-shirt or sweate) to $1.  Then a $10 gift certificate could buy the first list, but not the second.  Or you could set realistic prices, with the sweaters more expensive than the shirts, and the criteria would be met.