5. There are 30 vehicles consisting of motorcycles and cars in parking lot, the total amount of wheels of vehicles in the parking lot is 96 . If one car is charged Rp 3.500 .00 and motorcycles charged at Rp \( 2.000,00 \), the amount of money received is ...

Let's denote the number of motorcycles as \( m \) and the number of cars as \( c \). Given: 1. Total number of vehicles: \( m + c = 30 \) 2. Total number of wheels: \( 2m + 4c = 96 \) 3. Cost of one car: Rp 3,500 4. Cost of one motorcycle: Rp 2,000 We need to find the total amount of money received. Let's solve the system of equations to find the values of \( m \) and \( c \), and then calculate the total amount of money received. Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}m+c=30\\2m+4c=96\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}c=30-m\\2m+4c=96\end{array}\right.\) - step2: Substitute the value of \(c:\) \(2m+4\left(30-m\right)=96\) - step3: Simplify: \(-2m+120=96\) - step4: Move the constant to the right side: \(-2m=96-120\) - step5: Subtract the numbers: \(-2m=-24\) - step6: Change the signs: \(2m=24\) - step7: Divide both sides: \(\frac{2m}{2}=\frac{24}{2}\) - step8: Divide the numbers: \(m=12\) - step9: Substitute the value of \(m:\) \(c=30-12\) - step10: Simplify: \(c=18\) - step11: Calculate: \(\left\{ \begin{array}{l}c=18\\m=12\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}c=18\\m=12\end{array}\right.\) - step13: Rewrite: \(\left(c,m\right) = \left(18,12\right)\) The solution to the system of equations is \( c = 18 \) and \( m = 12 \). Now, let's calculate the total amount of money received: 1. Total number of cars: \( c = 18 \) 2. Total number of motorcycles: \( m = 12 \) The total amount of money received is: \[ 18 \times 3,500 + 12 \times 2,000 = 63,000 + 24,000 = 87,000 \] Therefore, the total amount of money received is Rp 87,000.