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.
+128473 Let the total number of skateboards = X
Let the total number of scooters = Y
And we know that
(1/4)X = (2/3)Y multiply both sides by 3/2
(3/8)X = Y
So fraction of red skateboards and scooters to the total =
[ 1/4X + (2/3)Y ] / [ X + Y ] =
[ 1/4X + 1/4X ] / [ X + (3/8)X ] =
[ (1/2) X ] / [ (8/8)X + (3/8)X ] =
[ (1/2)X ] / [ (11/8) X ] = (cancel the X's )
(1/2) / (11/8) = (invert the second fraction and multiply )
(1/2) * (8 /11) =
8 / 22 =
4 /11
