Find X and Y given two equal terms

Question

The Problem

The two following terms are equal:

$21x^2y^5= 35x^3y^4$

I was tasked with finding $\frac{x}{y}$

What I did:

$21x^2y^5= 35x^3y^4$

• I first divided both sides with $x^2$ which results in

$21y^5= 35x^1y^4$

• I then divided both sides with $y^4$ which results in

$21y^1= 35x^1$

• To get $\frac{x}{y}$ , I divided $\frac{35}{21}$ to result in $\frac{5}{3}$

HOWEVER my answer is wrong

The correct answer is $\frac{3}{5}$

Where have I gone wrong?

Answer 1

From the last equation

$$21y=35x $$ divide both sides by $35y $ to get

$$\frac {21y}{35y}=\frac {35x}{35y}=$$

$$\frac {21}{35}=\frac {x}{y}=\frac {3}{5} $$

Answer 2

The last step

$$21y = 35x$$

Dividing by $35y$ should give you

$$\frac{21}{35}=\frac{x}{y}$$

Remark: It is also possible for $\frac{x}y =0$.