(Since rubies are whole units, we know that the value for x will be a positive whole number. The King doesn’t have a fraction of a ruby, he just has ruby!)

The oldest daughter Clara gets 20% of the rubies, so 0.20*x

The King now has 100% – 20% of his rubies remaining to give to his other daughters, so 1.00*x – 0.20*x = 0.80x (80% of the original rubies)

The middle daughter Harriet gets 25% of the remaining rubies, so 0.25*0.80*x = 0.20*x

The King, after giving rubies to Clara and Harriet, now has 1.00*x – 0.20*x -0.20*x = 0.60*x (60% of the original rubies) remaining to give to his remaining daughter.

The youngest daughter, Melissa, gets 30% of the remaining rubies, so 0.30*(0.60*x) = 0.18*x

The King, after giving rubies to Clara, Harriet, and Melissa, now has 1.00*x – 0.20*x -0.20*x – 0.18*x = 0.42*x (42% of the original rubies) remaining.

There are 21 remaining rubies after giving them to all three daughters.

0.42*x = 21

21 is 42% of what number?

Now, we want to get the multiplier of x equal to 1 in order to figure out how many rubies (solve for x). We can add/subtract/multiply/divide the same amount to both sides of an equals equation and keep the equality. Here, we will divide both sides by 0.42.

(0.42*x)/0.42 = 21/0.42

x = 50

So the King originally had 50 rubies.

The oldest daughter Clara gets 20% of the rubies, so 0.20*x, or 0.20*50 = 10 rubies

There are now 50-10 = 40 rubies remaining

The middle daughter Harriet now gets 25% of the remaining rubies, so 0.25*40 = 10 rubies

There are now 50-10-10 = 30 rubies remaining

The youngest daughter now gets 30% of the remaining rubies, so 0.30*30 = 9 rubies

There are now 50-10-10-9 = 21 rubies remaining

yea! our numbers work, as the King had 21 rubies remaining in the original question.

To recap:

1. King originally had 50 rubies.

2. Oldest daughter Clara and middle daughter Harriet each get 10 rubies, and the youngest daughter Melissa gets 9 rubies.

he decided to give 20% so he’s left with 80%

after that he decided to give 25% of 80% so he’s left with 60% of the total rubies

moreover he distributed 30% of the 60% he had finally he has only 42% of the original left with him that totalled to 21

42x/100=21

x=50

King had total 50 rubies

First daughter share= 50*20%= 10

Second daughter share= 40*25%= 10

Third daughter share= 30*30% = 9

52.5 in total

10.5 each

its much easier to see it if you draw it out.

after he gave some rubies to Clara he had

(x – 0.20x) rubies left

after he gaveHarriet some rubies he had

(x – 0.20x)-0.25(x – 0.20x) rubies left

after he gave Melissa some rubies, he had

[(x – 0.20x)-0.25(x – 0.20x)] -0.3[(x – 0.20x)-0.25(x – 0.20x)] rubies left… which equaled 21

[(x – 0.20x)-0.25(x – 0.20x)] -0.3[(x – 0.20x)-0.25(x – 0.20x)] =21

0.75(x-0.20x) – 0.3[0.75(x-0.20x)] = 21

0.7 [0.75(x-0.20x)] = 21

0.7[0.75x(0.80)]=21

x=21/0.7/0.75/0.8

x= 30/0.75/0.8

x=40/0.8

x=50 rubies

Clara=0.20x = 10 rubies

Harriet=0.25(50-10) = 10 rubies

Melissa=0.30(50-10-10)= 9 rubies

10+10+9+21 = 50!