If 2/3x =4/5y =5/6z, what is x : y : z?

HELP PLEASE WILL GIVE BRAINLIEST BUT PLEASE ACTUALLY TRY!!!

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!

30 : 25 : 24

Step-by-step explanation:

2/3x =4/5y =5/6z

Let x = 1

2/3 = (4/5)y

y = 5/6

2/3 = (5/6)z

z = 4/5

x : y : z

1 : 5/6 : 4/5

Multiply by 30 ro remove fractions

30 : 25 : 24

yes

yes yes yes

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.