Question

mia works at a parking garage and is in charge of monitoring the number of vehicles parked daily. she knows the fee for cars is $8 and for motorcycles is $5. after collecting $198 from 30 vehicles that day, she wonders how many cars and motorcycles used the garage.

Answer 1

The total amount collected is indeed $198, which confirms that 16 cars and 14 motorcycles used the parking garage that day.

Explanation:

Let's use a system of equations to solve this problem.

Let C represent the number of cars and M represent the number of motorcycles.

We have two pieces of information:

The total number of vehicles parked daily is 30: C + M = 30.

The total amount collected is $198, where each car pays $8 and each motorcycle pays $5: 8C + 5M = 198.

Now, we can solve this system of equations. Let's use the substitution method.

From the first equation, we can express C as C = 30 - M.

Substitute this expression for C into the second equation:

8(30 - M) + 5M = 198

Now, distribute the 8:

240 - 8M + 5M = 198

Combine like terms:

240 - 3M = 198

Subtract 240 from both sides:

-3M = 198 - 240

-3M = -42

Now, divide by -3 to solve for M:

M = -42 / -3

M = 14

So, there were 14 motorcycles parked that day. Now, we can find the number of cars using the first equation:

C + M = 30

C + 14 = 30

Subtract 14 from both sides:

C = 30 - 14

C = 16

There were 16 cars parked that day.

To verify, let's check if the total amount collected matches the information:

Total amount collected = (Number of cars * Car fee) + (Number of motorcycles * Motorcycle fee)

Total amount collected = (16 * $8) + (14 * $5)

Total amount collected = $128 + $70

Total amount collected = $198

The total amount collected is indeed $198, which confirms that 16 cars and 14 motorcycles used the parking garage that day.