question in description

Question

A store sells used and new video games. New video games cost more than used video games. All used video games cost the same. All new video games cost the same.

Danny spent a total of $195 on 9 used video games and 3 new video games. Zoe spent a total of $98 on 6 used video games and 1 new video game. Jessica has $189 to spend.

Enter the number of used video games Jessica can purchase after she purchases 5 new video games.

Answer 1

Jessica can only purchase 2 Used Video Games

You can use a substitution here

Let x = Used Video games

Let y = New Video games

Danny's Purchase

9x + 3y = 195

Zoe's Purchase

6x + y = 98

y = 98 - 6x

If we substitute this for y in Danny's Purchase we have everything in terms of x and can solve for x

9x + 3(98 - 6x) = 195

9x + 294 - 18x = 195

Combine like terms

-9x + 294 = 195

Subtract 294 from both sides of the equation

-9x = 195 - 294

-9x = -99

Divide both sides of the equation by negative 9

x = -99/-9

x = 11

Used Video Games cost $11 each

Now we can solve for y where

y = 98 - 6x

y = 98 - 6(11)

y = 98 -66

y = 32

So New Videos cost $32 each

Checking in the original set up

9(11) + 3(32) = 195

99 + 96 = 95

6(11) + 32 = 98

66 + 32 = 98

Jessica has $189 to spend and she has purchased 5 new video games so

5(32) + x = 189

160 + x = 189

Subtract 160 from both sides of the equation to give

x = 189 - 160

x = 29

Since used video games are $11 each Jessica can only get 2 used video games

I hope you find this useful and if you have any questions please send me a message.