Need help w/ 'A king decided to give away part of his ruby c

[BR2010]

I need help with the following problem:

A King decided to give his daughters part of his Ruby collection. He first gave his daughter Andria 20% of his rubies; then he gave 25% of his remaining rubies to daugher Kathleen; then he gave 30% of his remaining rubies to his daughter Lydia. The King had 21 rubies left. How many rubies did the King have originally and how many rubies did he give each daughter? How would I go about solving this problem? Thanks for your help!

 

[TchrWill]

Re: Need help with this one

A King decided to give his daughters part of his Ruby collection. He first gave his daughter Andria 20% of his rubies; then he gave 25% of his remaining rubies to daugher Kathleen; then he gave 30% of his remaining rubies to his daughter Lydia. The King had 21 rubies left. How many rubies did the King have originally and how many rubies did he give each daughter?

Letting x stand for the starting amount,

x - 0.2x - 0.8x

0.8x - 0.25(0.8x) - 0.6x

0.6x - 0.3(0.6x) = 0.42x = 21

x = 50 rubies

 

[Mrspi]

Re: Need help with this one

I need help with the following problem:

A King decided to give his daughters part of his Ruby collection. He first gave his daughter Andria 20% of his rubies; then he gave 25% of his remaining rubies to daugher Kathleen; then he gave 30% of his remaining rubies to his daughter Lydia. The King had 21 rubies left. How many rubies did the King have originally and how many rubies did he give each daughter? How would I go about solving this problem? Thanks for your help!

Since you posted this on the algebra board, I will assume you want an algebraic way to solve it.

Let x = number of rubies the king had to begin with

He gave Andria 20% of the rubies, so he had 100% - 20%, or 80% of the rubies left. 80% of x is .8x.

Now, he gave Kathleen 25% of those rubies, and kept 100% - 25%, or 75% of them. So, he kept 75% of .8x, or .75(.8x), or .6x.

Finally he gave Lydia 30% of the rubies he had left. He kept 100% - 30%, or 70% of those rubies, so he kept 70% of .6x, or .7(.6x)......which is .42x

So, of the x rubies the king started with, he ended up with .42x rubies. And we know that he ended up with 21 rubies.

So,
.42x = 21

Solve that for x and you'll know how many rubies the king had to begin with. Then it should be easy to determine how many rubies each daughter received.

I hope this helps you. Note....it is possible to solve this problem using only arithmetic and common sense if you apply the "working backwards" method sometimes taught in problem-solving lessons.

 

[Denis]

Since 30% off means 70% remains, you can easily do these
in a continuous calculator operation, starting at bottom (21):

21 / .7 = 30 / .75 = 40 / .8 = 50

Just a "trick" :idea: