Justin got a sack of jelly beans in 5 different colors. Half of them were red, 1/6 were green, 1/6 were yellow, 1/12 were orange, and 6 were black. How many of each color did he get?

Red beans = 36 Green beans = 12 Yellow beans = 12 Orange beans = 6 Black beans = 6

Step-by-step explanation:

If we assume that "x" is the total number of beans:

Red beans: x/2 Green beans: 1/6 (x) = x/6 Yellow beans: 1/6 (x) = x/6 Orange beans: 1/12 (x) = x/12 Black beans = 6

So, the sum of all the beans:

x/2 + x/6 + x/6 + x/12 + 6 = x

Multiplying each term by 12:

(12) x/2 + (12) x/6 + (12) x/6 + (12) x/12 + (12) 6 = (12) x

6x + 2x+2x+x+72=12x

Isolating "x":

72 = 12x - 6x-2x-2x-x

72=x

Replacing the value of x in each equation of each bean:

Red beans: x/2: 72/2 = 36 Green beans: 1/6 (x) = x/6 = 72/6 = 12 Yellow beans: 1/6 (x) = x/6=72/6 = 12 Orange beans: 1/12 (x) = x/12 = 72/12=6 Black beans = 6