In the FreeWheelin' Skate Shop, exactly 1/4 of the skateboards are red and exactly 2/3 of the scooters are red. If there are equal numbers of red skateboards and red scooters in the shop, what fraction of the total skateboards and scooters together are red? Express your answer as a simplified fraction.
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Let the total number of skateboards be $4x$ and the total number of scooters be $3y$. Then, $\frac{1}{4}(4x) = \frac{2}{3}(3y)$, so $x=3y$. Then, the number of red skateboards is $x=\frac{3y}{3} = y$, and the number of red scooters is $y$. The total number of skateboards and scooters is $4x + 3y = 4(3y) + 3y = 15y$. The total number of red skateboards and scooters is $2y + y = 3y$. Therefore, the fraction of the total that is red is $\boxed{\frac{3y}{15y}} = \boxed{\frac{1}{5}}$.
1 answer