Solution:
Given:
[tex]y\propto x[/tex]
Introducing the constant of proportionality (k),
[tex]y=kx[/tex]
Substitute y = 12 and x = 15
[tex]\begin{gathered} 12=15\times k \\ 12=15k \\ \frac{12}{15}=k \\ k=\frac{12}{15} \end{gathered}[/tex]
Hence, the relationship is;
[tex]y=\frac{12}{15}x[/tex]
Find x when y = 21
[tex]\begin{gathered} 21=\frac{12}{15}x \\ 21=\frac{12x}{15} \\ Cross\text{ multiply;} \\ 12x=21\times15 \\ 12x=315 \\ x=\frac{315}{12} \\ x=\frac{105}{4} \end{gathered}[/tex]
Therefore,
[tex]x=\frac{105}{4}[/tex]
