[scientific222]

I am doing a chapter in my textbook about "Setting up equations in two unknowns" and there is a question I am stuck on, any help please:

A taxi company charges a fixed amount of £f plus x pence for each mile of a journey. A journey of 10 miles costs £10.20. A journey of 6 miles costs £7.40. Work out the cost of a journey of 8 miles.

The answer is 8.80 , I know this can be worked out without simultaneous equations however I have to use simultaneous equations to work it out in this chapter. I would be grateful for any help.

[TenOfThem]

The 10 mile journey gives this equation

100f + 10x = 1020

Then you make the equivalent other equation

[Intriguing Alias]

(Original post by TenOfThem)
The 10 mile journey gives this equation

100f + 10x = 1020

Then you make the equivalent other equation

Is it not 1000f?

[TenOfThem]

(Original post by hassi94)
Is it not 1000f?

Are there not 100 pence in a pound

[notnek]

(Original post by hassi94)
Is it not 1000f?

The £f is a fixed amount so the amount of pence corresponding to f for any distance will be 100f.

[Intriguing Alias]

(Original post by TenOfThem)
Are there not 100 pence in a pound

But then times by 10?

[TenOfThem]

(Original post by hassi94)
But then times by 10?

why?

that part is fixed

[Intriguing Alias]

(Original post by TenOfThem)
why?

that part is fixed

Oh sorry I misread massively. I thought it was 'f pounds + x pence' for each mile Didn't read 'fixed amount'.

[dannyoh]

Simultaneous Equations

10 miles: f + 10x = 10.2
6 miles: f + 6x = 7.4

4x = 2.8

x=0.7

f + 6x = 7.4

f + 4.2 = 7.4

f = 3.2

8 miles cost equals n, therefore: f + 6x = n

3.2 + (6 x 0.7) = 8.8

cost = £8.80

[notnek]

I don't really like the wording of this question because it seems to imply that f is a whole number when it actually isn't.

I think I would've doubted my answer if I did this question in an exam when I was a GCSE student. But maybe that's just me.

[scientific222]

(Original post by notnek)
I don't really like the wording of this question because it seems to imply that f is a whole number when it actually isn't.

I think I would've doubted my answer if I did this question in an exam when I was a GCSE student. But maybe that's just me.

It is tricky and it is only "A" grade, even the "A*" ones are easier.

[notnek]

(Original post by dannyoh)
Simultaneous Equations

10 miles: f + 10x = 10.2
6 miles: f + 6x = 7.4

4x = 2.8

x=0.7

f + 6x = 7.4

f + 4.2 = 7.4

f = 3.2

8 miles cost equals n, therefore: f + 6x = n

3.2 + (6 x 0.7) = 8.8

cost = £8.80

Full solutions are discouraged in this forum.

The OP has received enough info from other members to do the question himself which is much more beneficial than receiving a solution.

[dannyoh]

(Original post by notnek)
Full solutions are discouraged in this forum.

The OP has received enough info from other members to do the question himself which is much more beneficial than receiving a solution.

Sorry I'm not really a regular on the forum I didn't realise the rules regarding homework whatever & all the other info people posted was wrong

Feel free to delete it anyone

[TenOfThem]

(Original post by dannyoh)
Simultaneous Equations



x=0.7

In addition to being a full solution, this is not correct

Whilst it achieves the correct final answer that is because your error is later cancelled out

[TenOfThem]

(Original post by dannyoh)

Feel free to delete it anyone

The only person who can delete it is you

(or a mod)

but it would be easier for you

[scientific222]

Would this be correct:

100f + 10x = 10.20
100f + 6x = 7.40
x = 0.7
f = 3.2

And then 100f + 8x = cost
320 + 560 =8.8

[Intriguing Alias]

(Original post by dannyoh)
Sorry I'm not really a regular on the forum I didn't realise the rules regarding homework whatever & all the other info people posted was wrong

Feel free to delete it anyone

Actually your solution is wrong. You've given f and x the same 'weighting', if you will. Think about what you wrote in pounds and pence. You've wrote as if x is in pounds when it isn't. The mistake is consistent, though, so your answer is correct.

[notnek]

(Original post by scientific222)
Would this be correct:

100f + 10x = 10.20
100f + 6x = 7.40
x = 0.7
f = 3.2

And then 100f + 8x = cost
320 + 560 =8.8

You've made similar mistakes to dannyoh.

e.g. 100f + 10x = 10.20

Here, the left-hand-side is in pence and the right-hand-side is in pounds which is not what you want. Your units must be consistent in an equation like this.

Notice that if you follow your working properly then 8x=5.6 not 560 as you have written (the line in bold). What you should've got is

cost = 320+5.6 = 325.6

But this is not correct because of the earlier mistakes in your working.

[Namige]

This question doesn't make sense. Apparently x = 0.7 which is impossible as you can't get 0.7 pence. Surely it is £f + 10(£x) = 10.20?

[notnek]

(Original post by Namige)
This question doesn't make sense. Apparently x = 0.7 which is impossible as you can't get 0.7 pence. Surely it is £f + 10(£x) = 10.20?

That's not correct since x is in pence. And x pence = £ (x/100). So if you want to make the equation in terms of pounds, you should get:

£f + £(x/10) = £10.20