Writing and Solving Systems Given Word Problems (Systems of ... - Free Printable

Let’s solve this step by step.

We are told:
- Cars rent for $150 per day.
- Vans rent for $300 per day.
- Total vehicles rented = 30
- Total money made = $5700

We need to write a system of equations that represents this situation.

Step 1: Define variables (already given in the image)
Let:
- C = number of cars rented
- V = number of vans rented

Step 2: Write an equation for total vehicles.
Total vehicles = cars + vans → C + V = 30

Step 3: Write an equation for total money earned.
Money from cars = 150 × C
Money from vans = 300 × V
Total money = 150C + 300V = 5700

So our system is:
Equation 1: C + V = 30
Equation 2: 150C + 300V = 5700

Now let’s solve it to check if it makes sense.

From Equation 1: C = 30 - V

Plug into Equation 2:
150(30 - V) + 300V = 5700
→ 4500 - 150V + 300V = 5700
→ 4500 + 150V = 5700
→ 150V = 5700 - 4500 = 1200
→ V = 1200 ÷ 150 = 8

Then C = 30 - 8 = 22

Check:
Cars: 22 × $150 = $3300
Vans: 8 × $300 = $2400
Total = $3300 + $2400 = $5700 ✔
Total vehicles = 22 + 8 = 30 ✔

Everything checks out.

Final Answer:
The system of equations is:
C + V = 30
150C + 300V = 5700