#### bumblebee123

##### Junior Member

- Joined
- Jan 3, 2018

- Messages
- 200

Please, could someone help me out with a question in my daughters' Math book. The question relates to direct proportion and is given in the form of information. It seems quite straightforward and I see how they get the answer but it's not how I get the answer and I don't know why they choose to put the letters where they do. The answer I get is wrong but why? I have copied it out exactly:

Dave is working out different ways of travelling around Europe. He is making maps showing the cities he might visit. The time,

*T*minutes, that it takes Dave to draw a map is directly proportional to the square of the number of cities,

*c*, he puts on a map. A map with 8 cities takes 10 minutes to draw.

Question a) Find a formula for

*T*in terms of

*c*.

How I would answer:

I start with:

T = kc^2

( I use ^2 to stand for the square, so its c squared)

I substitute the known numbers for cities and time taken to draw:

10 = k8^2

I continue to solve:

10 = k64

10/64 = k

Substitute the k in to the formulae to give the answer:

T = 10/64c^2

so, T is equal to 10 divided by 64 multiplied by c squared.

However, this is not the answer, instead the answer in :

T = c^2/6.4

So I figure they have done: c^2 = kT

in order to get their answer. But why have they done this when the question says to find a formula for T in terms of c? How would I know to put the constant of proportionality next to Time and not cities?

Your thoughts would be much appreciated.

Thank you in advance.