11. An auto dealer sells motorcycles and Jeep \( 4 \times 4 \) 's. If he has 70 vehicles in his store, and a total of 226 tires, how many of each motor vehicle are there?

To tackle this puzzle, let's start by defining our variables. Let \( x \) be the number of motorcycles and \( y \) be the number of Jeep \( 4 \times 4 \) 's. We know two things: the total number of vehicles is 70 (so \( x + y = 70 \)) and the total number of tires is 226 (motorcycles have 2 tires each, while Jeeps have 4, leading to the equation \( 2x + 4y = 226 \)). Now, solving these equations together, we can substitute \( y \) from the first equation into the second equation. Doing the math, we'll find the values of \( x \) and \( y \) that represent the number of motorcycles and Jeeps in the store! By solving, we find \( y = 35 \) (Jeeps) and \( x = 35 \) (motorcycles). So, there are 35 motorcycles and 35 Jeeps in the store! This problem highlights how systems of equations can unlock real-world scenarios, like inventory challenges for businesses. It’s always fun to see math in action, don’t you think? If you're keen to brush up on algebra further, consider exploring books or online courses that focus on systems of equations. They'll offer you chances to practice with more engaging, real-life examples that sharpen your skills with every solution!