Suppose that y varies directly with x and inversely with z, and y = 18 when x = 15 and z = 5. Write the equation that models the relationship. Then find y when x = 21 and z = 7.

Y=18
Explanation:
the initial statement is
y
∝
x
z

to convert to an equation multiply by k the constant

of variation

⇒
y
=
k
×
x
z
=
k
x
z

to find k use the given condition

y
=
18
when
x
=
15
and
z
=
5

y
=
k
x
z
⇒
k
=
y
z
x
=
18
×
5
15
=
6

equation is
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
∣
∣
∣
2
2
y
=
6
x
z
2
2
∣
∣
∣
−−−−−−−−−−−−

when
x
=
21
and
z
=
7
then

y
=
6
×
21
7
=
18

The third box is a function

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