Question

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?

Answer 1

Answer:

• 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