if 8x=5y and 3y=14z then 12x= how many z's
5y = (5/3)(3y) = (5/3)(14z) = 70/3 z
12x = (3/2)(8x) = (3/2)(5y) = (3/2)(70/3)z = 35z
To find out how many z's are equivalent to 12x, we need to use the given equations and manipulate them to get the desired expression.
Given:
1) 8x = 5y
2) 3y = 14z
First, let's solve equation (1) for y by dividing both sides by 5:
8x / 5 = y
Now, substitute this expression for y into equation (2):
3 * (8x / 5) = 14z
Next, simplify the equation:
24x / 5 = 14z
To eliminate the fraction, cross-multiply the equation:
24x = 5 * 14z
24x = 70z
Finally, we can rearrange the equation to find out how many z's correspond to 12x. Divide both sides of the equation by 24:
(24x) / 24 = (70z) / 24
x = (70z) / 24
Now, we can substitute 12x back into the equation to solve for the equivalent number of z's:
12x = 12 * ((70z) / 24)
12x = (840z) / 24
Hence, 12x is equivalent to (840z) / 24, or, simplified further, 35z. Therefore, 12x is equal to 35z.