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The Problem

Lesley has a gift card worth $500 for a local entertainment store. Movies cost $20 each and newly released video games cost $50 each. In order to use the gift card, Lesley must purchase at least eleven items. Which is a combination of movies and newly released video games that Lesley could purchase using his gift card?

Answer provided by our tutors

let the number of movies = m and the number of games = g

set up 2 inequalities:

500 <= 20m + 50g 

m+g > 11

solve for m in the second

m > 11-g

substitute this into the first

500 <= 20(11-g) + 50g

500 <= 220-20g+50g

500 <=220 + 30g

280 <= 30g

9.33333 <=g so she can buy less than or equal to 9 games.

a possible combination would be 8 games and 11-8, or 3 movies, which would cost her the following:

20(3) + 50(8) = $60 + $400 = $460

*If you need more explanation feel free to message me :)

 

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