Multiply the second equation by 2: $ 4s + 10m = 370 $. Subtract the first equation: $ 3m = 55 \Rightarrow m = rac{55}{3} $. Substitute back: $ 2s + 5 \cdot rac{55}{3} = 185 \Rightarrow 2s = 185 - rac{275}{3} = rac{280}{3} \Rightarrow s = rac{140}{3} pprox 46.67 $. Convert to cents: $ 4667 $ cents.

["Multiply the Second Equation by 2: A Step-by-Step Solution to Solve for $ s $ and $ m $ (and Convert to Cents)", "When solving systems of linear equations, manipulating equations correctly can simplify the process and lead to accurate results. Today, we explore a classic approach: multiplying one equation and subtracting it from another to eliminate a variable. In this case, we begin with the system:", "$$\n\begin{align}\n4s + 10m &= 370 \quad \ ext{(Equation 1)} \\n3m &= 55 \quad \ ext{(Equation 2)}\n\end{align}\n$$", "### Step 1: Simplify Using the Second Equation\nWe're told to multiply the second equation by 2:", "$$\n2 \ imes (3m) = 2 \ imes 55 \Rightarrow 6m = 110\n$$", "Wait—this is incorrect based on the original. Instead, note Equation 2 states $ 3m = 55 $. Multiplying both sides of Equation 2 by 2 gives:", "$$\n2 \ imes (3m) = 2 \ imes 55 \Rightarrow 6m = 110 \quad \ ext{(Correct intermediate form)}\n$$", "But in the context of elimination, let's clarify: the goal is to eliminate $ m $ by subtracting scaled versions. However, from $ 3m = 55 $, the correct direct step is:", "$$\nm = \frac{55}{3}\n$$", "This follows immediately by dividing both sides by 3.", "### Step 2: Substitute $ m = \frac{55}{3} $ into Equation 1\nNow substitute into the first equation:\n$$\n4s + 10m = 370\n\Rightarrow 4s + 10 \left( \frac{55}{3} \right) = 370\n$$", "Calculate $ 10 \cdot \frac{55}{3} = \frac{550}{3} $, so:", "$$\n4s + \frac{550}{3} = 370\n\Rightarrow 4s = 370 - \frac{550}{3} = \frac{1110}{3} - \frac{550}{3} = \frac{560}{3}\n$$", "Now divide both sides by 4:", "$$\ns = \frac{560}{3} \div 4 = \frac{560}{3} \cdot \frac{1}{4} = \frac{140}{3} \approx 46.67\n$$", "### Step 3: Convert Final Answer to Cents\nSince the context involves money, we express $ s $ in cents:", "$$\n\frac{140}{3} \ ext{ dollars} = \frac{140}{3} \ imes 100 = \frac{14000}{3} \ ext{ cents} \approx 4666.\overline{6} \ ext{ cents}\n$$", "Rounded to the nearest whole number:\n4667 cents", "---", "This method—multiply one equation to align coefficients, substitute, then solve—shows how careful algebraic manipulation yields precise numerical results, essential when working with currency or physical measurements. Whether $ s $ and $ m $ represent quantities in cents or units, accurate step-by-step solving ensures reliability.", "Key Takeaways:\n- Always verify operations when scaling equations\n- Solve decimals or fractions precisely\n- Convert final numerical answers appropriately for context", "Effortless numbers, accurate results—mastering algebra step-by-step brings clarity to real-world problems."]