Answer:
30 : 25 : 24
Step-by-step explanation:
Notice the denominators of the fractions:
3 from 2/3x
5 from 4/5y
6 from 5/6z
Let's find their least common multiple (LCM): the LCM(3, 5, 6) = 3 * 5 * 2 = 30
Now, multiply 30 to each term:
30 * (2/3x) = 30 * (4/5y) = 30 * (5/6z)
20x = 24y = 25z
Let's prime factorize each of these terms:
2 * 2 * 5 * x = 2 * 2 * 2 * 3 * y = 5 * 5 * z
In order for these to be equal to each other, we must find numbers to fit the variables x, y, and z that will create a true statement. Notice that we have at most three 2s, one 3, and two 5s.
In order to make the x side have that many of each number, we need to multiply it by 2, 3, and 5. That means x = 2 * 3 * 5 = 30.
In order to make the y side have that many of each number, we need to multiply it by two 5s. That means y = 5 * 5 = 25.
Finally, in order to make the z side have that many of each number, we need to multiply it by three 2s and one 3. That means z = 2 * 2 * 2 * 3 = 24.
Thus, x : y : z = 30 : 25 : 24.
Hope this helps!
