31.8k views
22 votes
Steve bought used and new video games from a website. The new games cost $54 each and the used games cost $9 each. He spent no more than $243 on the video games and he bought no more than 7 video games. Let x represent the number of new video games, and let y represent the number of used video games. Identify an ordered pair that is a solution to the system of inequalities. Interpret the meaning of the ordered pair within the context of the problem by selecting the appropriate explanation.

User Sam Basu
by
3.6k points

1 Answer

2 votes

Answer:

y = 3 used games

x = 4 new games

Explanation:

54x + 9y = 243

x + y = 7 then x = 7 - y

substitute for x:

54(7 - y) + 9y = 243

378 - 54y + 9y = 243

reduce:

378 - 45y = 243

subtract 243 from each side:

135 - 45y = 0

add 45y to each side:

45y = 135

divide both sides by 45:

y = 3

x = 7 - 3 = 4

check:

3+4 = 7

7 = 7

54(4) + 9(3) = 243

243 = 243

User Lior Ohana
by
3.1k points