Question

Assume that y varies directly with x, then solve. No need to show work.

Answer 1

Given:

`y\propto x`

Introducing the constant of proportionality (k),

`y=kx`

Substitute y = 12 and x = 15

`\begin{gathered} 12=15* k \\ 12=15k \\ (12)/(15)=k \\ k=(12)/(15) \end{gathered}`

Hence, the relationship is;

`y=(12)/(15)x`

Find x when y = 21

`\begin{gathered} 21=(12)/(15)x \\ 21=(12x)/(15) \\ Cross\text{ multiply;} \\ 12x=21*15 \\ 12x=315 \\ x=(315)/(12) \\ x=(105)/(4) \end{gathered}`

Therefore,

`x=(105)/(4)`