Question

Please help me on this one question! (10th grade level)

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.

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.

Answer 1

Make an inequality representing both constraints.
0.5x+y<20
x+y≥24
for a

Answer 2

Let x represent the number of magnets and y represent the number of key chains.

She must purchase at least 24 gifts but has to spend less than $20.

x + y >= 24

0.5x + y < 20

An appropriate solution is x=20 and y=5. They satisfy both inequalities:

x + y = 25 so it is more than 24.

0.5x + y = 15 so it is less than 20.