Final answer:
To find the number of cars and motorcycles in the garage, set up a system of equations based on the given information. Then solve the equations to find the values of c (number of cars) and m (number of motorcycles). The number of cars is 7 and the number of motorcycles is 6.
Step-by-step explanation:
To find the number of cars and motorcycles in the garage, we can set up a system of equations based on the given information. Let's assume the number of cars is 'c' and the number of motorcycles is 'm'.
From the first sentence, we have c + m = 13 (equation 1).
From the second sentence, we know that each car has 4 tires and each motorcycle has 2 tires. So, the total number of tires can be expressed as 4c + 2m = 40 (equation 2).
To solve for c and m, we can use substitution or elimination. I will use the substitution method.
From equation 1, we can express c = 13 - m.
Substitute this into equation 2: 4(13 - m) + 2m = 40.
Simplify and solve for m: 52 - 4m + 2m = 40.
Combine like terms: -2m = -12.
Divide by -2: m = 6.
Substitute m = 6 into equation 1 to find c: c + 6 = 13.
Subtract 6 from both sides: c = 7.
So, there are 7 cars and 6 motorcycles in the garage.