Question

If x varies directly with y and y is 10 when x is 8, what is x when y is 18?

Answer 1

y varies directly with x
y=kx
10=k(15)
k=10/15
y=(10/15)x
when x=6
y=(10/15)(6)=60/15=4
x varies inversely as y
x=k/y
2=k/8
k=16
x=16/y
when y=17

Answer 2

Knowing that x varies directly with y, we know the basic skeleton of the equation is y = mx.

To find m, plug in the known coordinate (8,10), where the x-coordinate is 8 and the y-coordinate is 10.

`y=mx \\ 10=m8 \\ (10)/8=(8m)/8 \\ m= (10)/(8) = (5)/(4)`

Then, plug in m to the equation to get y = (5/4)x.

Finally, plug in the y-coordinate 18 to the equation and solve for x!

`y= (5)/(4)x \\ 18= (5)/(4)x \\ (4)/(5)(18)=( (5)/(4)x) (4)/(5) \\ x= (4*18)/(5) \\ x= (72)/(5)`

Your exact answer is x = 72/5. However, if your teacher prefers decimals, then x = 14.4

Hope this helps!