Question

There are white, blue, and red boats in a marina. Three-fourths of the boats in the marina are white, 4 7 of the remaining boats are blue, and the rest are red. If there are 9 red boats, how many boats are in the marina?

Answer 1

84 boats

Explanation:

3/4 are white

1 -3/4 = 1/4

1/4 of the boats are either red or blue

4/7 of the the 1/4 or blue

4/7 * 1/4 = 1/7

1/7 of the total boats are blue

x is the fraction of red boats

The fractions, when added up, equals 1

3/4 + 1/7 +x =1

The common denominator is 28, so multiply each side by 28

28 (3/4 + 1/7 +x) =1*28

Distribute

28 *3/4 + 28 *1/7 +28x =28

21 + 4 + 28x = 28

Combine like terms

25 + 28x = 28

Subtract 25 from each side

25-25 +28x= 28-25

28x = 3

Divide each side by 28

x =3/28

White: Blue: Red

3/4 1/7 3/28

This is the fraction. We need the number of boats so multiply by y

3/4y 1/7y 3/28y

We know there are 9 red boats

That means 3/28 *y = 9

Solve for y

3/28 y =9

Multiply by 28/3 on each side

28/3 * 3/28 y = 9 * 28/3

y = 84

The number of each type of boat is

White: Blue: Red

3/4 *84 1/7*84 3/28*84

63 12 9

We want the total number of boats

63+12+9

84