Question

Justin got a sack of Jelly beans in 5 different colors. Half if 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, and how many jelly beans were there in all

Answer 1

Answer:

Total number of Jelly beans in the sack = 72

Number of red beans = 36

Number of green beans = 12

Number of yellow beans = 12

Number of orange beans = 6

Number of black beans = 6

Step-by-step explanation:

Let total number of jelly beans be =$x$

We are given fractions of different colors of beans. To find the exact number of beans we need to multiply the fraction with the total number of beans.

Fraction of total are red beans = $\frac{1}{2}$

Number of red beans = $\frac{1}{2}\times x= \frac{x}{2}$

Fraction of total are green beans = $\frac{1}{6}$

Number of green beans = $\frac{1}{6}\times x= \frac{x}{6}$

Fraction of total are yellow beans = $\frac{1}{6}$

Number of yellow beans = $\frac{1}{6}\times x= \frac{x}{6}$

Fraction of total are orange beans = $\frac{1}{12}$

Number of orange beans = $\frac{1}{12}\times x= \frac{x}{12}$

Number of black beans = 6

Total number of beans can be given as

$\frac{x}{2}+\frac{x}{6}+\frac{x}{6}+\frac{x}{12}+6$

Since we assumed total number of beans to be $x$, so we have.

$\frac{x}{2}+\frac{x}{6}+\frac{x}{6}+\frac{x}{12}+6=x$

Multiplying each term by 12 to remove fractions.

$(12\times\frac{x}{2})+(12\times\frac{x}{6})+(12\times\frac{x}{6})+(12\times\frac{x}{12})+(12\times6)=12\times x$

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

combining like terms.

$11x+72=12x$

Subtracting both sides by $11x$

$11x+72-11x=12x=11x$

$72=x$

∴ $x=72$

Total number of Jelly beans in the sack = 72

Number of red beans = $\frac{1}{2}\times 72= 36$

Number of green beans = $\frac{1}{6}\times 72= 12$

Number of yellow beans = $\frac{1}{6}\times 72= 12$

Number of orange beans = $\frac{1}{12}\times 72= 6$

number of black beans = 6