# Find two numbers, given their difference and quotient

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?

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.

• I was able to formulate these exact equations, however I was not able to follow through with actually logically processing the steps needed to solve the math by elimination. – rickyjoepr Jan 18 '15 at 22:35
• I know I have 4y/x=5, now I am combing videos how to eliminate the variable and solve – rickyjoepr Jan 18 '15 at 22:37

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.
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?
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 $x=1\frac{1}{4}$.