Linear equation word problem

Question

"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 $147$.

Answer 1

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 $147 - x$.