Find two numbers, given their difference and quotient

Question

The difference between two numbers is 3. If four times the smaller is divided by the larger, the quotient is 5. Find the numbers.

I am strengthening my math, practicing on my own time. Can you please help me understand how the formula for this problem is created?

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Solved: I answered the question using substitution. I chose an equation, then isolated one variable, after Isolating the variable I substituted it into the other equation.

Answer 1

Let your two numbers be $x$ and $y$, with $x>y$. Then $x-y=3$. We also know that $\frac{4y}{x}=5$.

You can then isolate for either $x$ or $y$ in one of the equations. Then substitute this in the other equation and solve for the remaining variable.

Answer 2

Denote $x$ and $y$ the two numbers $x<y$ so we have

$$y-x=3\quad;\quad 4x=5y$$ Can you take it from here?

Answer 3

Let $x$ and $y$ be the two numbers. $x-y=3$, $x$ is the larger and $y$ is the smaller, $y < x$. Then $\frac{4y}{x}=5\to{}\frac{4y}{x}=\frac{5}{1}\to{}4y=5x\to{}y=1\frac{1}{4}x$. Let for example $y=1$ then $x=1\frac{1}{4}$.