Question

Please help me with this math question​

Answer 1

d : e : f = 4 : 3 : 6

Explanation:

`\bold{METHOD\ 1}\\\\6d=8e\qquad\text{divide both sides by 6}\\\\d=(8)/(6)e\to d=(4)/(3)e\\\\\text{Substitute it and}\ f=2e\ \text{to the ratio}\ d:e:f:\\\\(4)/(3)e:e:2e\qquad\text{cancel}\ e\\\\(4)/(3):1:2\qquad\text{multiply by 3}\\\\\huge\boxed{4:3:6}`

`\bold{METHOD\ 2}\\\\6d=8e\qquad\text{divide both sides by 6}\\\\d=(8)/(6)e\qquad\text{divide both sides by}\ e\\eq0\\\\(d)/(e)=(4)/(3)\to d:e=4:3\\\\2e=f\qquad\text{divide both sides by 2}\\\\e=(f)/(2)\to e=(1)/(2)f\qquad\text{divide both sides by}\ f\\eq0\\\\(e)/(f)=(1)/(2)\to e:f=1:2\\\\\text{We have}\ d:e=4:3\ \text{and}\ e:f=1:2.`

`\text{We know}\ (1)/(2)=(1\cdot3)/(2\cdot3)=(3)/(6)\\\\\text{threfore}\ e:f=3:6\\\\\text{Now we have}\\\\\left\begin{array}{ccc}d:e=4:3\\e:f=3:6\end{array}\right\}\large{\boxed{d:e:f=4:3:6}}`