Have a sack of jelly beans-5 different colors-half are red 1/6 green 1/6 yellow 1/12 blue 6 black-how many of each color and how many in all
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To determine the number of jelly beans of each color, we can start by finding the total number of jelly beans in the sack.
First, let's calculate the number of jelly beans that are red. We know that half of the jelly beans are red, so we can divide the total number of jelly beans by 2:
Red Jelly Beans = (Total Jelly Beans) / 2
Next, let's calculate the number of jelly beans that are green. We are given that 1/6 of the jelly beans are green, so we can calculate:
Green Jelly Beans = (Total Jelly Beans) * (1/6)
Similarly, for yellow jelly beans:
Yellow Jelly Beans = (Total Jelly Beans) * (1/6)
For blue jelly beans:
Blue Jelly Beans = (Total Jelly Beans) * (1/12)
For black jelly beans, we are given that there are 6:
Black Jelly Beans = 6
Finally, to find the total number of jelly beans, we can sum up the jelly beans of each color:
Total Jelly Beans = Red Jelly Beans + Green Jelly Beans + Yellow Jelly Beans + Blue Jelly Beans + Black Jelly Beans
You can substitute the given values and calculate the individual quantities and the total number of jelly beans.
Let x = total number
x - 1/2x - 1/6x - 1/6x - 1/12x = 6
Solve for x and then the fractions.