Katie is buying souvenir gifts for her big family back home. She wants to buy everyone either a key chain or a magnet. The magnets are on sale for 50 cents each and the key chains cost $1 each. She must purchase at least 24 gifts but has to spend less than $20. Let x represent the number of magnets and y represent the number of key chains.

Question

A. Model the scenario with a system of inequalities.
B. Graph the system of inequalities and choose an appropriate solution for the scenario. Use complete sentences to prove why the solution is appropriate. It is optional to include your graph as part of your final answer.

Answer 1

0.50x + 1.00y <= 20.00
x >= 1
y >= 1
x+y >= 24
The graph is found at

https://www.wolframalpha.com/input/?i=plot+0.50x+%2B+1.00y+%3C%3D+20.00,+x+%3E%3D+1,+y+%3E%3D+1,+x%2By+%3E%3D+24

Any integer values for x and y in the shaded region is a solution to your problem. For example, (25,5)
where
she bought 30 items
the cost is 12.50 + 5.00 = 17.50

Answer 2

John is at a local bait shop; he wants to buy bait for his fishing trip. At the store, they are selling live bait for $12 a pound and natural bait for $7 a pound. John would like to get at least 3 pounds of live bait, but he only has a budget of $63. Let x be the amount of live bait and y be the amount of natural bait. Model the scenario with a system of inequalities.