1. **State the problem:** We need to find two numbers whose sum is 178 and one number is 84 more than the other. 2. **Set variables:** Let the smaller number be $x$. 3. **Express the larger number:** Since one number is 84 more than the other, the larger number is $x + 84$. 4. **Write the sum equation:** The sum of the two numbers is 178, so: $$x + (x + 84) = 178$$ 5. **Simplify the equation:** $$2x + 84 = 178$$ 6. **Isolate $x$:** Subtract 84 from both sides: $$2x + \cancel{84} - \cancel{84} = 178 - 84$$ $$2x = 94$$ 7. **Solve for $x$:** Divide both sides by 2: $$\frac{2x}{\cancel{2}} = \frac{94}{\cancel{2}}$$ $$x = 47$$ 8. **Find the larger number:** $$x + 84 = 47 + 84 = 131$$ 9. **Answer:** The smaller number is $47$ and the larger number is $131$. **Note:** The user's provided answers (larger number 94, smaller number 84) do not satisfy the sum condition $94 + 84 = 178$; actually, $94 + 84 = 178$ is true but 94 is not 84 more than 84. The correct solution is as above.