Algebra Word Math Problem (Easier)

[Kristina123]

Three co-workers, Arden, Dale, and Ryan, received an innovation award for their ground breaking work on battery technology.
They have decided to split the award as follows:

(i) Arden receives $10 000 plus 1/5 of what then remains;
(ii) Dale then receives $16 000 plus 1/4 of what then remains; and
(iii) Ryan then receives the rest, which is $18 000. How much is the original monetary award?

Which co-worker receives the most money?

 

[Deleted member 4993]

Three co-workers, Arden, Dale, and Ryan, received an innovation award for their ground breaking work on battery technology.
They have decided to split the award as follows:

(i) Arden receives $10 000 plus 1/5 of what then remains;
(ii) Dale then receives $16 000 plus 1/4 of what then remains; and
(iii) Ryan then receives the rest, which is $18 000. How much is the original monetary award?

Which co-worker receives the most money?

Please follow the rules of posting in this forum, as enunciated at:

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Please share your work/thoughts about this assignment.

 

[HallsofIvy]

This harder than it look! It appears to me that "what then remains" depends on who get paid first.
Let "x" be the total amount.

If Arden is paid first: Arden receives "$10,000 plus 1/5 of what then remains" so Arden gets $10,000+ 0.2(x- 10,000)= 8,000+ 0.2x. That leaves 0.8x- 8,000. Now Dale receives "$16,000 plus 1/4 of what then remains" so Dale gets $16,000+ 0.25(0.8x- 8000- 16,000)= 0.2x+ 10,000. That leaves 0.8x- 8,000- 0.2x- 10,000= 0.6x- 18,000 for Ryan and we are told that is $18,000. Solve 0.6x- 18,000= 18,000 for x.

On the other hand, if Dale is paid first, Dale receives "$16,000 plus 1/4 of what remains" so Dale receives 16000+ 0.25(x- 16000)= 0.25x+ 12,000. That leaves x- (0.25x+ 12,000)= 0.75x- 12,000. Now Arden, being paid second, receives "$10,000 plus 1/5 of what then remains" so $10,000+ 0.2(0.75x- 12,000)= 0.15x- 7600. That leaves 0.75x- 12,000- (0.15x- 7600)= 0.6x- 4,400 for Ryan and we are told that is $18,000. Solve 0.6x- 4400= 18000 for x. I am inclined to thing the first way was intended and this whole second calculation was unnecesary!

 

[Dr.Peterson]

I think the word "then", which is used repeatedly, makes the sequence of events clear.

@Kristina123, please show some work before expecting any additional help.

 

[Kristina123]

I think the word "then", which is used repeatedly, makes the sequence of events clear.

@Kristina123, please show some work before expecting any additional help.

I tried solving the equation where x was 70 000. But when I finished solving it, the three answers did not add up to 70 000. I don't even know if I'm converting the word problem into the correct math equation. I don't know how to get to the answer. Please help me.

 

[Steven G]

I tried solving the equation where x was 70 000. But when I finished solving it, the three answers did not add up to 70 000. I don't even know if I'm converting the word problem into the correct math equation. I don't know how to get to the answer. Please help me.
View attachment 14603

The work you did will only work with only one particular x. Can you please state why you used 70,000 for x?
Also your work from the 1st to 2nd line is not correct. Please don't write that 24,000=18,000, PLEASE!

As Dr Halls suggested, to get the correct value for x you need to solve 0.6x- 18,000= 18,000 for x.
Try to solve this equation and please show us your work.

 

[Dr.Peterson]

What you are doing here is not solving an equation. Rather, you are practicing how to check your answer at the end, supposing that you found that the answer was 70 000. The fact that the numbers don't add up just shows that your guess of 70 000 is not the correct answer.

So let's move to the next step. Replace 70 000 in your work with the variable x, representing the unknown total amount. (That is, go back to the equation HallsofIvy wrote.) What you need to do is to solve that equation (the equation at the end of his work, not the expression at the start.) You do know what solving an equation means, right? It means to find the value of x that makes it true.

 

[Kristina123]

What you are doing here is not solving an equation. Rather, you are practicing how to check your answer at the end, supposing that you found that the answer was 70 000. The fact that the numbers don't add up just shows that your guess of 70 000 is not the correct answer.

So let's move to the next step. Replace 70 000 in your work with the variable x, representing the unknown total amount. (That is, go back to the equation HallsofIvy wrote.) What you need to do is to solve that equation (the equation at the end of his work, not the expression at the start.) You do know what solving an equation means, right? It means to find the value of x that makes it true.

I think I understand how to solve the problem now. Can you check over my work and see if it is correct? I've also checked my answer at the end using x as 60,000.

If everything is fine, could you please help me with my next word problem. Again, I don't know how to solve it, nor even start the problem. I assume you would want to see my work for that problem as well, but I don't know how to start it. Could you help me and guide me step by step on what to do for that problem?
https://www.freemathhelp.com/forum/threads/algebra-math-word-problem.119005/#post-472340

 

[tkhunny]

Did you check your answer to see that it actually follows the path you specified while you were calling it "x"?

In this way, you can check your own work and move on with greater confidence.