Jessica has several red, white, and black marbles in her pocket. If she draws a marble out of her pocket without looking, the probability of drawing a red marble is

2

5

,

the probability of drawing a white marble is

1

10

,

and the probability of drawing a black marble is

1

2

.

How many marbles of each color could she have? Show your work.

Step-by-step explanation:

P (red) = 2/5

P (white) = 1/10

P (black) = 1/2

The number of marbles in her pocket must be a multiple of 5, 10, and 2. The least common multiple (LCM) of these three numbers is 10.

If she has 10 marbles in her pocket, then:

red = 2/5 (10) = 4

white = 1/10 (10) = 1

black = 1/2 (10) = 5

She could have 4 red marbles, 1 white marble, and 5 black marbles.