Derive an expression for the price of a pen in terms of p

[Richie Smash]

Homework Statement

Hello there are two types of pens expensive and cheap.
The ratio of the prices of the two is 3:7
The total cost for 30 of the cheaper pens and 10 of the expensive pens is $1568.

I am asked to derive an expression for the cost of ONE of the expensive pens which i will represent as (e) in terms of one of the cheap pens as (p)

Homework Equations

30p+10e =$1568

The Attempt at a Solution

So this is what i originally thought,

30p +`10e =1568
SO : 10e= 1568-30p
e= (1568-30p)/10

But I think this is terribly wrong as they asked for the price of one of the expensive pens in (p)...

And their answer (my textbook) is 7/3p.

So I'm thoroughly confused. What key concept am I missing?

 

[phinds]

So I'm thoroughly confused. What key concept am I missing?

Most likely the key concept that textbooks sometimes get it wrong.

 

[Alloymouse]

You can attempt to express the price of expensive in terms of price of cheap pens

You know the ratio 3:7, hence p/e = 3/7

From there, you should be able to get your answer. I'm guessing there's another part of this question that asks you to solve for the individual prices p and e.

 

[Richie Smash]

Yes alloy mouse, there is and I've already solved it using their answer (7/3)p =e
And indeed it makes the equation 30p+10e =$1568 true.

My problem is deriving it, ratios are tricky yes, I'm not sure how to get my answer, I think I lack a fundamental understanding about ratios.

 

[Alloymouse]

Yes alloy mouse, there is and I've already solved it using their answer (7/3)p =e
And indeed it makes the equation 30p+10e =$1568 true.

My problem is deriving it, ratios are tricky yes, I'm not sure how to get my answer, I think I lack a fundamental understanding about ratios.

Ah I see, so it's the problem with ratios.Here's a trick:

If price of cheap pen is 3 units,
Price of expensive pens is 7 units

If you treat ratios like "this has x units while the other has y units", that would make things easier to see and easier to derive your "(7/3)p = e"

 

[Richie Smash]

SO let me see if I have this now, let's say the ratio was 5:10, the price of a cheap pen would be (5/10)e and the price of an expensive pen would be (10/5)p.
DO I have this concept correct now?

 

[Alloymouse]

SO let me see if I have this now, let's say the ratio was 5:10, the price of a cheap pen would be (5/10)e and the price of an expensive pen would be (10/5)p.
DO I have this concept correct now?

Yes, you are right!