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"Separate $147$ into two numbers so that the larger number exceeds three times the smaller by $27.$"

I'm supposed to use only one variable, to devise an equation consistent with the above information, then solve for the larger and smaller numbers that add up to $147$.

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    $\begingroup$ Call the smaller $s$. write an equation for the larger, but hide it from your teacher. Then substitute that into larger+smaller=147 and claim victory. $\endgroup$ Oct 12, 2016 at 22:32

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Call $x$ the larger number; then $147-x$ is the smaller number.
Since the larger number exceeds three times the smaller number by $27$, We have the equation $$x = 3(147-x) +27$$ $$\text{or}\,4x = (3\cdot 147) +27$$ I'm assuming you can solve the above equation for $x$, the larger number, and then the smaller number will be $147 - x$.

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