Question

Nina wants to download games for her video game console. Older games cost 500points and new releases cost 2000 points. Nina has 20,000 points to use. The equation 500a+2000b=20,000, where a is the number of older games and b is the number of new releases, models the situation. How many older games can she download if she downloads one new game? four new games?

Answer 1

Well if she downloads one new game she can get 36 new games, because 20,000-2,000=18,000 18,000 divided by 500= 36. If she bought four new games she can get 24 new games because 4•2,000=8,000 20,000-8,000= 12,000 12,000 divided by 500=24

Answer 2

Nina could buy 36 old games if she buys 1 new game.

Nina could buy 24 old games if she buys 4 new game.

Explanation:

Cost of older games = 500 points

Cost of new games = 2000 points

Nina uses the equation:

`500a + 2000b = 20000`

to download games, where a is the number of older games, b is the number of new games.

a) Nina downloads 1 new game.

Thus, b = 1

Putting this value in the equation:

`500a + 2000 = 20000\\500a = 20000-2000\\500a = 18000\\a = 36`

Thus, Nina could buy 36 old games if she buys 1 new game.

b) Nina downloads 4 new game.

Thus, b = 4

Putting this value in the equation:

`500a + 4* 2000 = 20000\\500a = 20000-8000\\500a = 12000\\a = 24`

Thus, Nina could buy 24 old games if she buys 4 new game.