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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.

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3 Answers

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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?

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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.

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

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