1550.28 – Swerve's Bikes and Skateboards

Swerve, the local bicycle store, bought some used bikes and skateboards to overhaul and re-sell. If they paid an average of $55 per bike and $22 per skateboard, AND if they bought twice as many bikes as skateboards, AND if they spent a total of $660, how many of each did they buy?

Solution

Let xx be the number of skateboards and 2x2x be the number of bikes.

Then Swerve paid $22x\text{\textdollar}22x for the skateboards and $55(2x)\text{\textdollar}55(2x) for the bikes.

And all of that comes out to $660$, thusly:

$22x+$55(2x)=$22x+$110x=$132x=$660,\text{\textdollar}22x + \text{\textdollar}55(2x) = \text{\textdollar}22x + \text{\textdollar}110x = \text{\textdollar}132x = \text{\textdollar}660,

so x=5x = 5. That's 5 skateboards and 10 bikes.

Note: for anyone worrying about the "average" price, it just means you can assume they were all the same price and it all comes out OK--$55 for each bike and $22 for each skateboard.