ML had \( \$ 12.50 \) more than Miss Mak. 21 Miss Leee hiss Lee spent \( \$ 18 \), Miss Mak had 3 times as much money as After Mish left. Miss Lee had left. How much money did Miss Lee have at first?

To solve this problem, we need to set up a system of equations based on the given information. Let's denote the amount of money Miss Lee had at first as \( L \). From the information given: 1. Miss Lee had \( \$12.50 \) more than Miss Mak. 2. Miss Mak had 3 times as much money as Miss Lee after Miss Lee spent \( \$18 \). We can set up the following equations based on these conditions: 1. \( L = 12.50 + M \) (where \( M \) is the amount of money Miss Mak had) 2. \( M = 3(L - 18) \) Now, we can solve this system of equations to find the initial amount of money Miss Lee had. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}L=12.5+M\\M=3\left(L-18\right)\end{array}\right.\) - step1: Substitute the value of \(L:\) \(M=3\left(12.5+M-18\right)\) - step2: Simplify: \(M=-16.5+3M\) - step3: Move the variable to the left side: \(M-3M=-16.5\) - step4: Subtract the terms: \(-2M=-16.5\) - step5: Change the signs: \(2M=16.5\) - step6: Divide both sides: \(\frac{2M}{2}=\frac{16.5}{2}\) - step7: Divide the numbers: \(M=\frac{33}{4}\) - step8: Substitute the value of \(M:\) \(L=12.5+\frac{33}{4}\) - step9: Simplify: \(L=\frac{83}{4}\) - step10: Calculate: \(\left\{ \begin{array}{l}L=\frac{83}{4}\\M=\frac{33}{4}\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}L=\frac{83}{4}\\M=\frac{33}{4}\end{array}\right.\) - step12: Rewrite: \(\left(L,M\right) = \left(\frac{83}{4},\frac{33}{4}\right)\) The solution to the system of equations is: \( L = 20.75 \) and \( M = 8.25 \). Therefore, Miss Lee had \( \$20.75 \) at first.