Stumper help please???

Question

A king decided to share his collection of precious rubies with his three daughters. He gave his oldest daughter, Clara, 20% of the rubies. He gave Harriet, his middle daughter, 25% of those that were left. He gave his youngest daughter, Melissa, 30% of the remaining rubies.After each daughter had received her share, the king saw that there were 21 rubies left in his collection.

1. how many rubies did the king have in his collection to begin with?

2. how many did each daughter receive?




i asked my brother to help me but he was busy with his own homework. i basically asked everyone of my friends and family,but no luck in helping me. please can someone help me? can you also explain how you got the answer to it??

Answer 1

The King starts with x rubies, or 100% of the x rubies, or 1.00*x
(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.

Answer 2

Suppose king has 100% of 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

Answer 3

he gave clara 1/5, then gave harriet 1/4 of whats left (1/4 of whats left is 1/5 of the total), then gave melissa 1/3 of whats left (1/3 of what's left is 1/5 of the total). so if you minus it all out, 1 - 1/5 -1/5 -1/5 = 2/5. since he had 21 left, 21 divide by 2, times 5 = 52.5.

52.5 in total
10.5 each

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

Answer 4

I will give you some help but not solve it for you. You need to set up a set of simultaneous equations with a variable set up for each unknown quantity equalling some set number that you do know. First you solve for any one variable, then substitute in to solve for the second, third, etc. Once you solve the whole thing, plug in your answers and see if they satisfy the original questions.

Answer 5

let x=rubies he started with:
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!

Answer 6

well, i'm terribly sorry that i'm horrible at math...but, i hope you get the answer!