Question

The variables y and x have a proportional relationship, and y=9 when x=2. What is the value of y when x=3?

Answer 1

I believe it should be 3

Answer 2

For this case we have that by definition, if the variables "y" and "x" have a proportional relation, and
`y = 9`when
`x = 2`, then:

`\frac {x} {y} = \frac {2} {9}`

Now, we want to know the value of the variable "y" when
`x = 3`, then:

`\frac {3} {y} = \frac {2} {9}`

Clearing "y" we have:

We multiply by "y" on both sides of the equation:

`y * \frac {3} {y} = y * \frac {2} {9}\\3 = \frac {2y} {9}`

We multiply by 9 on both sides:

`9 * 3 = \frac {2y} {9} * 9\\27 = 2y`

We divide by 2 on both sides:

`\frac {27} {2} = \frac {2y} {2}\\y = 13.5`

So, when
`x = 3`then
`y = 13.5`

Answer:

`y = 13.5`