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\begin{align*}\$22x + \$55(2x) &= \$22x + \$110x \\&= \$132x \\&= \$660\end{align*}

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.