Parking

One hundred twenty vehicles are parked in the morning. Passenger car is charged 20 CZK and 50 CZK per bus. The guard collected for parking 2640 CZK in total. How many cars and buses stood in the parking?

Correct answer:

a =  112
b =  8

Step-by-step explanation:

20 a+50 b=2640 a+b=120  20⋅ a+50⋅ b=2640 a+b=120  20a+50b=2640 a+b=120  Row2−201​⋅ Row1→Row2 20a+50b=2640 −1.5b=−12  b=−1.5−12​=8 a=202640−50b​=202640−50⋅ 8​=112  a=112 b=8

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Showing 1 comment:
Dr. Math
To determine the number of cars and buses parked, let’s define:
- x = number of cars
- y = number of buses

We are given:
1. The total number of vehicles is 120:
 
  x + y = 120
 

2. The total parking fee collected is 2640 CZK:
 
  20x + 50y = 2640
 

Step 1:

Solve for One Variable
From the first equation:
x = 120 - y

Step 2:

Substitute into the Second Equation
Substitute x = 120 - y into the second equation:
20(120 - y) + 50y = 2640

2400 - 20y + 50y = 2640

2400 + 30y = 2640

Step 3:

Solve for y
Subtract 2400 from both sides:
30y = 240

Divide by 30:
y = 8

Step 4:

Solve for x
Substitute y = 8 into x = 120 - y :
x = 120 - 8 = 112

Step 5:

Verify the Solution
Check the total parking fee:
20(112) + 50(8) = 2240 + 400 = 2640 CZK

This matches the given total.

Final Answer:


- Number of cars:

112


- Number of buses:

8






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