In a bag of small balls 1/4 of the balls are green, 1/8 are blue, 1/12 are yellow and the remaining 26 are white. How many balls are blue?

Thursday, August 20, 2015

In a bag of small balls 1/4 of the balls are green, 1/8 are blue, 1/12 are yellow and the remaining 26 are white. How many balls are blue?

Let's denote the total number of the balls in a bag by x. Then,

the number of the green balls is $\displaystyle\frac{{1}}{{4}}{x}$ ,

the number of the blue balls is $\displaystyle\frac{{1}}{{8}}{x}$ ,

the number of the yellow balls is $\displaystyle\frac{{1}}{{12}}{x}$

and the number of the white balls is 26, is given. The total number of balls, x, equals the sum of the balls of all colors:

$\displaystyle\frac{{1}}{{4}}{x}+\frac{{1}}{{8}}{x}+\frac{{1}}{{12}}{x}+{26}=\ldots$

Let's denote the total number of the balls in a bag by x. Then,

the number of the green balls is $\displaystyle\frac{{1}}{{4}}{x}$ ,

the number of the blue balls is $\displaystyle\frac{{1}}{{8}}{x}$ ,

the number of the yellow balls is $\displaystyle\frac{{1}}{{12}}{x}$

and the number of the white balls is 26, is given. The total number of balls, x, equals the sum of the balls of all colors:

$\displaystyle\frac{{1}}{{4}}{x}+\frac{{1}}{{8}}{x}+\frac{{1}}{{12}}{x}+{26}={x}$

To solve this equation, we can first multiply the both sides by the least common denominator of all fractions. The least common multiple of 4, 8 and 12 is 24. Multiplying both sides by 24 results in

6x + 3x + 2x + 26*24 = 24x

11x + 26*24 = 24x

26*24 = 13x

To find x, divide both sides by 13. Since 26/13 = 2, we get

x = 2*24 = 48.

The total number of the balls is 48. Since the number of the blue balls is 1/8 of the total number, there are 48/8 = 6 blue balls.

There are 6 blue balls in the bag.

Notes

Thursday, August 20, 2015