Need a spell check on an algebra word problem

A group of tourists reserved... As a group, more than 1, tourist should be pluralized.

If 6 additional tourists had participated...

...each participant would have paid $10 less. (The sentence can end here, no reason or need to add 'then he actually paid.)
Additionally, your use of 'then', should have been than.

...if 10 of the tourists had cancelled...

...what is the total price of... Price being singular. Additionally, you could substitute the word cost in place of price.

A group of tourists reserved a bus for a trip. If 6 additional people had participated, each participant would have paid $10 less than they did. On the other hand, if 10 had canceled, each participant would have needed to add $30 extra. How many tourists are in the group, and what is the total price of the trip?

Edited for grammar, unnecessary words, repetition etc.

If 6 additional tourists would have participated in the trip,

if 10 of the tourists would have canceled their participation,

================

Addressed to Sturgis and Centrox.

What is the reason for the change from 'would' to 'had'? Is it a change that is compulsory in English grammar?

Aren't 'could'/'should'/'were to' possible as replacements for 'would' and 'had'?

Why is 'would' proscribed here?

I'm not saying possible as in reflecting the same meaning or that they are a perfect fit for the words they are paired with in this particular case but I think we can all envision a scenario where they would work.

If 6 additional tourists could/should/were to have participated in the trip,

if 10 of the tourists could/should/were to have canceled their participation,

"Would have" for "had" is a very common (mainly US) error.

"If I would have locked the door, then the burglar would not have got in". The first "would have" is an example. It should be "had".

When talking about something in the past that didn't happen, many English speakers use the conditional perfect (if I would have done) when they should be using the past perfect (if I had done).

For example, you find out that your brother saw a movie yesterday. You would have liked to see it too, but you hadn't known he was going. To express this, you can use an if - then clause. The correct way to say this is with the past perfect in the "if" clause, and the conditional perfect in the "then" clause:

Correct: If I had known you were going to the movies, [then] I would have gone too.

The conditional perfect can only go in the "then" clause -- it is grammatically incorrect to use the conditional perfect in the "if" clause:

Incorrect: If I would have known you were going to the movies, I would have gone too.

More examples:

Correct: If I had gotten paid, we could have traveled together.

Incorrect: If I would have gotten paid, we could have traveled together.

Correct: If you had asked me, I could have helped you.

Incorrect: If you would have asked me, I could have helped you.

I don't believe just stating it is incorrect is helpful, Centrox. You didn't address the part in quotes, above.

Your example:

"If I would have locked the door, then the burglar would not have got in".

"If I COULD have locked the door, [actual situation: the lock was broken] then the burglar would not have got in".

"If I COULD lock the door, then the burglar would not have got in".

[actual situation: the lock IS broken and has been for some time. first part describes this general condition]

The reason I say this is that we all know that the written language and the spoken language are different. They each have their own rules of grammar. Well, that isn't exactly true.

The written language has its own set of conventions, at least some of which are not real rules of English grammar.

The original question is about an algebra problem expressed in words. It includes a situation in which some things which might have happened didn't happen, and how that would have affected a situation also in the past - if more or fewer people had joined the trip, they would have paid more or less money. In this situation, 'had' is correct, and 'would have' is not. I invented an example in which something that might have happened (I locked the door) simply didn't happen. As a result my house was burgled. Could/would/should are not possible as replacements for that. If you want to invent scenarios in which these would have been, then you are welcome to do so.

Thank you Sir. Really appreciate your help

Tanks Sir. This was very helpful

Correct: If I had gotten paid, we could have traveled together.

Incorrect: If I would have gotten paid, we could have traveled together.

Correct: If you had asked me, I could have helped you.

Incorrect: If you would have asked me, I could have helped you.

The ones that you list as "incorrect" are not that at all. They are more emotive than the 'had' variant.

For "if he would have" Google Scholar notes About 14,700 results.

Title: “I Wish I Would Have Known!”: The Usage of Would Have in Past Counterfactual If- and WishClauses Journal Issue: Issues in Applied Linguistics, 14(1) Author: Ishihara, Noriko, University of Minnesota Publication Date: 2003

http://escholarship.org/uc/item/5wd0w3sz#page-1

What are the answers that you obtain to the word problem, and are those answers what you wanted to achieve in setting the question Nate?

Hi,
The answers are:
There are 30 tourists in the group.
The total price of the trip is $1800.
Thanks for the help,
Kind Regards,
Nathan

It's back to the classroom for you I'm afraid Nate.

The answer to the problem is P = (5/2)*N -15
(where P is the price of each ticket and N is the number of trippers)

viz. N=20, P=35
......N=14, P=20
......N=30,P=60



You and I travel to the beat of a diff'rent drum.
Oh, can't you tell by the way I run
Ev'ry time you make eyes at me. Wo oh.
You cry and you moan and say it will work out.
But honey child I've got my doubts.
You can't see the forest for the trees.

Was Mike Nesmith part of the Stone Poneys?

No. They just covered a song he wrote.

.. and let's not forget, his mother, Bette Nesmith who created LiquidPaper (a.k.a. Whiteout), which, has helped bad typists quite a bit.

Wouldn't it have been grand if she had invented a "Whiteout" which could help bad grammarians quite a bit, Sturgis? And the science deniers and bad science advancers also?

Isn't a "cover" defined as a second recording of an original recording?

In truth it was first recorded/filmed whathaveya in 1966 as part of The Monkees television show, performed by Nesmith. Linda Ronstadt and the Stone Poneys did their version in 1967.