Finding and simplifying a formula

[Probability]

So I'm really struggling with the understanding of how to interpret the English questions being asked when trying to create a formula. This is a serious lack of experience on my part, but is there a way of interpreting the questions to create the math formulas in a straight forward type of way.

In this question I was asked;

A machine company charges £250 to print 400 labels of an agreed size. If further labels are then required another agreement is to charge an extra £0.25 per label.

I'm asked to find a formula for the cost C of printing the labels, assuming that (n) is at least 400. I've been working on this on and off most of the day, and I don't find this type of math easy to work out. I decided that C would be the total cost and (n) would be the cost of additional labels. I eventually came up with this formula;

[MATH]{C}={250}+{0.25}({n}-{400})[/MATH] I then was asked to simplify the formula;

[MATH]{C}={250}+{0.25n}-{100}=[/MATH]
[MATH]{C}={150}+{0.25n}[/MATH]
I was then asked to use the formula to find the cost of another 450 labels.

[MATH]{C}={150}+{0.25}\times{450}=[/MATH]
[MATH]{C}={150}+{112.50}=£287.50[/MATH]

 

[lev888]

I decided that C would be the total cost and (n) would be the cost of additional labels.

Based on your work it seems n is the total number of labels, not cost(?!) of additional labels.
Looks good to me until the last addition.

 

[HallsofIvy]

So I'm really struggling with the understanding of how to interpret the English questions being asked when trying to create a formula. This is a serious lack of experience on my part, but is there a way of interpreting the questions to create the math formulas in a straight forward type of way.

In this question I was asked;

A machine company charges £250 to print 400 labels of an agreed size. If further labels are then required another agreement is to charge an extra £0.25 per label.

I'm asked to find a formula for the cost C of printing the labels, assuming that (n) is at least 400. I've been working on this on and off most of the day, and I don't find this type of math easy to work out. I decided that C would be the total cost and (n) would be the cost of additional labels. I eventually came up with this formula;

[MATH]{C}={250}+{0.25}({n}-{400})[/MATH] I then was asked to simplify the formula;

[MATH]{C}={250}+{0.25n}-{100}=[/MATH]
[MATH]{C}={150}+{0.25n}[/MATH]

ASSUMING n is greater than 400 to begin with this is correct.

I was then asked to use the formula to find the cost of another 450 labels.

[MATH]{C}={150}+{0.25}\times{450}=[/MATH]
[MATH]{C}={150}+{112.50}=£287.50[/MATH]

I wonder exactly what "another 450 labels" means. You seem to have assumed it mean a total of 400+ 450 labels. I think I would have interpreted it as meaning only the cost of the 450 labels over the first 400 or more. That would be just 0.25(450)= £137.50.

 

[Otis]

I wonder exactly what "another 450 labels" means …

I think it means they placed a second order for labels. (The first order was for 400 labels.)

C = 0.25(n) + 150

So, I've assumed that C is the cost of each order placed. (The minimum quantity per order is 400 labels.)

It would be nice to see the given information. Maybe the word 'another' doesn't even appear.

?

 

[Probability]

ASSUMING n is greater than 400 to begin with this is correct.


I wonder exactly what "another 450 labels" means. You seem to have assumed it mean a total of 400+ 450 labels. I think I would have interpreted it as meaning only the cost of the 450 labels over the first 400 or more. That would be just 0.25(450)= £137.50.

Thank you for pointing that mistake out to me, yes you are correct, the word "another" came freely from me and was not written in the question. I was asked to use the formula to find the cost of printing 450 labels. Sorry about that, but the formula has been simplified above so we must remember that C = 150 + 112.50 = £262.50.

This is however incorrect; That would be just 0.25(450)= £137.50.

Looking back through my original post it appears I've pressed the wrong key on the keyboard when I wrote;

C =150+112.50=287.50. Clearly I should have wrote £262.50. Sorry about that my mistake.