Find the constant of variation and write the equation representing the relationship between the given quantities, if z varies jointly as x and y.
1. z =27, x =3 and y =3
constant of variation: k = 3
equation of variation: z = 3xy
z = kxy
27 = k(3)(3)
27 = k(9)
27/9 = k
k = 3
2. z =50, x = 5, and y =2
constant of variation: k = 5
equation of variation: z = 5xy
z = kxy
50 = k(5)(2)
50 = k(10)
50/10 = k
k = 5
3. z =60, x =2, and y =15
constant of variation: k = 2
equation of variation: z = 2xy
z = kxy
60 = k(2)(15)
60 = k(30)
60/30 = k
k = 2
4. z =8, x =4, and y =3
constant of variation: k = 2/3
equation of variation: z = (2/3)xy
z = kxy
8 = k(4)(3)
8 = k(12)
8/12 = k
k = 2/3
5. z =100, x =5, and y=4
constant of variation: k = 5
equation of variation: z = 5xy
z = kxy
100 = k(5)(4)
100 = k(20)
100/20 = k
k = 5
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