Problema Solution
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. If Lesley wants to spend as much as possible on his gift card by purchasing the most items, which combination of movies and newly released video games is optimal?
Answer provided by our tutors
let the number of movies = m and the number of games = g
set up 2 inequalities:
20m + 50g <= 500 multiply both sides by 1/10
2m + 5g <= 50
m+g > 11
solve for m in the last
m > 11-g
substitute this into 2m + 5g <= 50
2(11-g) + 5g < 2m + 5g <= 50
22 - 2g + 5g < 50
22 + 3g < 50
g < 28/3 < 9.33
g <=9 so she can buy less than or equal to 9 games.
possible combinations would be
9 games and 2 movies since 20*2 + 9*50 = 490 < 500
8 games and 5 movies since 20*5 + 5*50 = 500
7 games and 7 movies since 20*7 + 7*50 = 490
6 games and 10 movies since 20*10 + 6*50 = 500
5 games and 12 movies since 20*12 + 5*50 = 490
4 games and 15 movies since 20*15 + 4*50 = 500
3 games and 17 movies since 20*17 + 3*50 = 490
2 games and 20 movies since 20*20 + 2*50 = 500
1 game and 22 movies since 20*22 + 1*50 = 490
Maximum items Lesley can purchase and spend as much as possible on his gift card is 23 items (1 game and 22 movies and spend total of $490).