Solve Height Puzzle: Find Davina's Height Using Algebraic Equations

[Natasha1]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

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

 

[berkeman]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

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

Maybe P+D+A = 300

P-D = D-A

Are those two equations enough to get the solution?

 

[Natasha1]

P = 2D - A

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

How do I get P and A?

 

[physics user1]

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?

 

[physics user1]

P = 2D - A

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

How do I get P and A?

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

 

[Natasha1]

D-100=A-100

So D = A which is wrong??

 

[berkeman]

2D= P+A

(P+A)+D= 300

D-100=A-100

Just re-check your algebra...

 

[Natasha1]

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

Is this correct?

 

[phinds]

Is this correct?

Does it give the right answer?

 

[Samy_A]

P = 2D - A

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

So Davina is 100 cm tall, that is correct.

How do I get P and A?

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

 

[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?

Hint: look at your algebra, it'll be easier to think about this algebraically than from just reading the problem text (which is what you're asking for, correct?).

 

[HallsofIvy]

Homework Statement

Pritesh is taller than Davina who is taller than Alicia.

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

The difference in height between Pritesh and Davina is the same as the difference in height between Davina and Alicia.

So P- D= D- A.

The total of their heights is 300 cm. How tall is Davina?

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.

2. Homework Equations

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

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".

3. The Attempt at a Solution

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

 

[Natasha1]

Thank you everyone, I have understood