Marc and Aki are building hot wheels tracks. Marc has 4-inch pieces to make his track, and Aki has 10-inch pieces to make his track. How long will their tracks be when they are first the same length?(1 point) Responses 30 inches 30 inches 20 inches 20 inches 40 inches 40 inches 50 inches
The length of the tracks will be first the same when the total length of the track built by Marc is equal to the total length of the track built by Aki.
We can find the length of the track built by Marc by multiplying the number of 4-inch pieces he has by 4 inches: Marc's track length = 4 inches/piece * number of pieces.
Similarly, we can find the length of the track built by Aki by multiplying the number of 10-inch pieces he has by 10 inches: Aki's track length = 10 inches/piece * number of pieces.
Let's denote the number of pieces Marc has as M and the number of pieces Aki has as A.
We are given that the length of Marc's track is equal to the length of Aki's track, so we can write the equation:
4M = 10A
To find the smallest numbers that satisfy this equation, we need to find the lowest common multiple (LCM) of 4 and 10.
The LCM of 4 and 10 is 20, so the length of their tracks will be equal to 20 inches when they are first the same length. Answer: 20 inches.