Question

A video game system and several games are sold for $644. The cost of the games is 3 times as much as the cost of the system find the cost of the system and the games

Answer 1

The cost of the games is $483, and the cost of the system is $161.

Explanation:

Firstly represent this as an equation:

Let
`x` represent the total cost of the games (the total cost of all the games combined, because we aren't told how many games there are)

&

Let
`y` represent the total cost of the system.

So:


`x + y = 644`

We're told that the cost of the games is 3 times the cost of the system. What this means is we can represent the cost of the system in terms of the cost of the games. Because we defined the cost of the system as
`y`, this must mean,
`x`, the cost of the games, is equal to 3 times y. (
`x = 3y`)

So replacing
`x` with
`3y` in the equation we get:

`3y + y = 644`

Now that we have one variable, we can solve.

`4y = 644`

`(4y)/(4) = (644)/(4) \\\\y = 161`

We found that
`y`, the cost of the system; is $161.

Now hold on, how do we find the cost of the games (
`x` ) ?

Recall earlier how we defined
`x=3y`. We now know what
`y` is, so we can simply substitute it in.

`x = 3y`

`x = 3(161) = 483`

Now we've completely solved!

The cost of the games is $483, and the cost of the system is $161.

Strange prices, but thats how the question sets it up!

Key Points to Remember

1. List all variables.
2. Make an equation using those variables.
3. Try to express all variables as one variable.

4. Solve for that variable.

5. Use the value found there to solve for the other variables.