Combined Variation
[tex]\bold{r=\frac{ks}{t}}\:\:,\:\:\sf s=\frac{rt}{k}\:\:,\:\:\sf t=\frac{ks}{r}\:\:,\:\:\sf k=\frac{rt}{s}[/tex]
Given:
r=27, when s=18 and t=2
Find the constant (k)
[tex]\begin{aligned}&\sf k=\frac{rt}{s}\\&\sf k=\frac{27(2)}{18}\\&\sf k=\frac{54}{18}\\&\sf k=3\end{aligned}[/tex]
Use k=3 to solve the following
1. r when t=3 and s=27
[tex]\begin{aligned}&\sf r=\frac{ks}{t}\\&\sf r=\frac{\cancel3\times 27}{\cancel3}\\&\boxed{\bold{\purple{r=27}}}\end{aligned}[/tex]
2. s when t=2 and r=3
[tex]\begin{aligned}&\sf s=\frac{rt}{k}\\&\sf s=\frac{\cancel3\times 2}{\cancel3}\\&\boxed{\bold{\purple{s=2}}}\end{aligned}[/tex]
3. t when r=1 and s=6
[tex]\begin{aligned}&\sf t=\frac{ks}{r}\\&\sf t=\frac{3\times 6}{1}\\&\boxed{\bold{\purple{t=18}}}\end{aligned}[/tex]
4. r when s=4 and t=2
[tex]\begin{aligned}&\sf r=\frac{ks}{t}\\&\sf r=\frac{3\times \cancel4}{\cancel2}\\&\sf r=3\times 2\\&\boxed{\bold{\purple{r=6}}}\end{aligned}[/tex]
5. s when t=5 and r=6
[tex]\begin{aligned}&\sf s=\frac{rt}{k}\\&\sf s=\frac{\cancel6 \times 5}{\cancel3}\\&\sf s=2\times 5\\&\boxed{\bold{\purple{s=10}}}\end{aligned}[/tex]
