Difference in heights

1. Jan 2, 2016

Natasha1

1. The problem statement, all variables and given/known data

Pritesh is taller than Davina who is taller than Alicia. The difference in height between Pritesh and Davina is the same as the difference in height between Davina and Alicia. The total of their heights is 300 cm. How tall is Davina?

2. Relevant equations

Now trial and error gives me Alicia = 50cm, Davina = 100cm and Pritesh = 150cm as the difference between them is 50cm

3. The attempt at a solution

How could I do this problem using only algebra, rather than what I did with trial and error?

2. Jan 2, 2016

Staff: Mentor

Maybe P+D+A = 300

P-D = D-A

Are those two equations enough to get the solution?

3. Jan 2, 2016

Natasha1

P = 2D - A

So substituting gives
2D - A + D + A = 300
3D = 300
D = 100

How do I get P and A?

4. Jan 2, 2016

Cozma Alex

Hi, let's write these info:

P+A+D= 300
D-P=A-D

You need D

Look at the second equation, you can write it as: 2D= P+A , that's amazing

Look at the first : (P+A)+D= 300

Can you see it?

5. Jan 2, 2016

Cozma Alex

You can't, you need another equation, but you only need D

6. Jan 2, 2016

Natasha1

D-100=A-100

So D = A which is wrong??

7. Jan 2, 2016

8. Jan 2, 2016

Natasha1

P-D = D-A
so
P - 100 = 100 - A
P = 200 - A
A = 200 - P

Is this correct?

9. Jan 2, 2016

phinds

Does it give the right answer?

10. Jan 3, 2016

Samy_A

So Davina is 100 cm tall, that is correct.
You don't have enough information to answer that question. That's why you are only asked how tall Davina is.

11. Jan 3, 2016

Thewindyfan

Can you remember a technique that allows you to deal with more than one unknown quantity, and can you recognize the quantity you do not need to answer this question?

12. Jan 3, 2016

HallsofIvy

Staff Emeritus
Let P be the Pritesh's height, in cm, D be Davina's height in cm., and A be Alicia's height in cm.

So P- D= D- A.

And A+ D+ P= 300. That give two equations, P- D= D- A and A+ D+ P= 300 to solve for three unknowns. That is not enough information. We need one more equation. We Could write P- D- A as 2D= P+ A and replace "P+ A" in the second equation by 2P to get 2D+ D= 3D= 300 to get D= 100. But putting D= 100 in either of the two equations gives P- 100= 100- A so that A+ P= 200.

Yes, that is one solution. But taking, say, A= 40, P= 200- 40= 160 also satisfies A+ P= 200 so also satisfies "P- D= 160- 100= 60" and "D- A= 100- 40= 60". Or taking A= 25, P= 200- 25= 175, which also satisfies A+ P= 200 as well as "P- D= 175- 100= 75" and "D- A= 100- 25= 75".

13. Jan 4, 2016

Natasha1

Thank you everyone, I have understood