Question

Given the equations x = 6y, 4y = 9z, and (3x)(9z) = ky, what is the value of k in terms of y, if y ≠ 0?

Answer 1

72y

Explanation:

To find the value of 3x in terms of y, multiply both sides of the equation x = 6y by 3: 3x = 18y. Also, since 4y = 9z, by the Commutative Property, 9z = 4y. Therefore, by substitution, (18y)(4y) = ky, or 72y22 = ky, and if both sides of the equation are divided by y, the value of k is shown to be 72y.

Answer 2

x=6y
x/6=y
4y=9z
(4/9)y=z
4(x/6)=9z
(2/3)x=9z
x(2/3)/9=z
(2/27)x=z
(3x)(9z)=ky
(3(6y))(9((4/9)y))=k(y)
(18y)(4y)=k(y)
(72y^2)=k(y)
y(72y)=y(k)
72y=k