Finding the ratio of $\frac{x}{z}$

Question

$x,y,z \in \mathbb R$ and $x,y,z \neq 0$

$$2x = 5y$$ If $$\frac{y}{3} = \frac{z}{4}$$

Find the ratio of $\frac{x}{z}$

Let me show what I thought

We have

$$2x = 5y$$

Which means that we should give $5k$ for $x$, and $2k$ for $5y$

Thus we get

$$\frac{3k}{y}= \frac{z}{4}$$

Sorry If I've gone too wrong.

Answer 1

Hint: From $2x=5y$ you have that $y=\frac{2}{5}x$, and from $\frac{y}{3}=\frac{z}{4}$ you have that $\frac{y}{z}=\frac{3}{4}$

Answer 2

$$2x=5y$$ $$\Rightarrow y=\frac {2x}{5}$$ $$\frac y3=\frac z4\Rightarrow \frac {x}{15}=\frac z8$$ $$\Rightarrow \frac xz=\frac {15}{8}$$

Answer 3

It is : $y=\frac{2}{5}x$ so simply by substituting :

$$\frac{\frac{2}{5}x}{3} = \frac{z}{4} \Leftrightarrow \frac{x}{z} = \frac{15}{8}$$

Answer 4

We have $$2x=5y\implies \color{red}{x=\frac52}\color{blue}y$$ and $$\frac{y}{3} = \frac{z}{4}\implies \color{blue}{y=\frac34z}$$ so $$\color{red}{x=\frac52}\cdot\color{blue}{\frac34z}\implies \boxed{\frac xz=\frac{15}8}$$

Answer 5

An option:

1)$2x=5y,$ divide both sides by by $2z:$

1') $x/z = (5/2)(y/z).$

2)$y/3=z/4$, then

2')$ y/z = 3/4$ (why?)

Substuting 2') into the RHS of 1'):

$x/z= (5/2)(3/4)=15/8.$