Mr. Rich had 2 times more cars than motorcycles in his garage. After he bought 1 more car and sold 2 motorcycles, there were 3 times more cars than motorcycles. How many cars and motorcycles were there in garage?

After the sale there were 15 cars and 5 motorcycles

Step-by-step explanation:

c=cars originally

m=motorcycles originally

c=2m (2 times the cars than motorcycles)

(c+1) bought 1 car after sale

sold 1 motor cycle (m-2) after sale

(c+1) = 3 (m-2) (3 times more cars than motorcycles)

(c+1) = 3 (m-2)

distribute

c+1 = 3m-6

substitute c = 2m

2m + 1 = 3m-6

subtract 2m from each side

2m+1-2m = 3m-6-2m

1 = m-6

add 6 to each side

1+6 = m-6+6

m=7

c = 2m

c = 2 (7) = 14

c=14

Originally there were 7 motorcycles and 14 cars

After the sale c+1 = 15, m-2 = 5

there were 15 cars and 5 motorcycles

In the Garage, Numeber of cars are 15 and Number of motorcycles are 5

Step-by-step explanation:

let number of motorcycles be = x

he had 2 times more cars than motorcycles so, no of cars = 2x

he bought 1 more car, so number of cars = 2x+1

he sold 2 motorcycles, so motorcycles = x-2

he had 3 times more cars than motorcycles so, we equate it like this:

3 (x-2) = 2x+1

solving the equation

3x-6 = 2x+1

here we find, x=7

solving for no of cars:

2x+1

2 (7) + 1

no of cars = 15

solving for no of motorcycles:

x-2

7-2

no of motorcycles = 5