Need eqns for: At what price does it become less expensive

[Math_Mark]

There are two companies that sell widgets. Both companies sell the widgets to the general public for the same price. In order to earn business, Company A offers a special 25% discount on each order. In response, Company B offers a 35% discount on every dollar the customer spends over $50. Both discounts are rounded to the nearest cent. If you place an order for $50 or less, it is less expensive to order from Company A. If you place a large enough order, it will be less expensive to order from Company B. At what price does it become less expensive to order from Company B?

Determine algebraically the actual price at which Company B offers you the same discount as Company A. Make sure to show all relevant work.

Determine the actual price at which Company B will give you a greater discount than Company A.

1. Explain how you reached this conclusion.

Not sure I understand that last question. Wouldn't it be one penny more than where the two prices meet? Is that too obvious?

I am not really good at creating my own equations from a word problem like this. If anyone can give me a hand and help me learn in the process, it would be greatly appreciated!
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Edited by stapel -- Reason for edit: Let's keep things friendly, okay? Thank you!

 

[Mrspi]

Re: Need an equation for a word problem...

There are two companies that sell widgets. Both companies sell the widgets to the general public for the same price. In order to earn business, Company A offers a special 25% discount on each order. In response, Company B offers a 35% discount on every dollar the customer spends over $50. Both discounts are rounded to the nearest cent. If you place an order for $50 or less, it is less expensive to order from Company A. If you place a large enough order, it will be less expensive to order from Company B. At what price does it become less expensive to order from Company B?

Determine algebraically the actual price at which Company B offers you the same discount as Company A. Make sure to show all relevant work.

Determine the actual price at which Company B will give you a greater discount than Company A.

1. Explain how you reached this conclusion.

What have you tried to do to solve this problem? Have you defined a variable to represent an unknown quantity in the problem? That's a very good first step.

Once you've defined that variable, see if you can "translate" the conditions stated in the problem to mathematical expressions or sentences.

I'd suggest that you write an expression to represent the cost of an order at company A, and another expression to represent the cost of an order at company B.

Then, you're asked to determine what order amount it would take for the cost at company B to be less than the cost at company A. So, you'll use the expressions you've already written to create an inequality:

company B cost < company A cost

Now....you try your hand at this problem. If you are still having trouble, repost showing us everything you've tried, even if you think it is wrong. That way, we can see where your difficulties might lie.

I hope this helps you.

 

[Math_Mark]

Thanks for the help and suggestions.

I have broken this into two separate equations.

Company A gives a 25% discount on any purchase.

Company B gives a 35% discount on any dollar spent after the first 50.00.

P = price

X = P(.75)

Y= P-50(.65)+50

So, let me just start there. Are those properly written?

If they are, I am not quite sure how to fit it all together. I need to know the precise amount that companies a and b are the same price. I will keep working it out and see if I can get it.

 

[Math_Mark]

I think maybe I was thinking from the wrong end. I need to find the price where the discount is equal. The way I had it written was to find where the price paid was equal. Once I find where the dicsount is equal, I will have the price, which I believe is 175. I just need the equation to find it.

So, now I have two equations:

P(.25)

P-50(.35)

Can someone give me the steps to solve for the above?

I guess I can graph it but I am not sure how to put the above together in a more statndard way.

I can do P(.25) = P-50(.35), but not sure that is right, or how to solve.

Any help would be greatly appreciated.

 

[Mrspi]

Thanks for the help and suggestions.

I have broken this into two separate equations.

Company A gives a 25% discount on any purchase.

Company B gives a 35% discount on any dollar spent after the first 50.00.

P = price

X = P(.75)

Y= P-50(.65)+50

So, let me just start there. Are those properly written?

If they are, I am not quite sure how to fit it all together. I need to know the precise amount that companies a and b are the same price. I will keep working it out and see if I can get it.

You need to "fix" Y by adding some parentheses. Since the discount is only on the amount OVER $50 for company B, you will receive the discount on (P - 50) dollars of your order:

Y = (P - 50)(.65) + 50

Ok....

Now, if the amount of the discounts you receive from each company are EQUAL, wouldn't you expect the cost of your order to be the same at each company?

cost at company A = cost at company B

.75P = (P - 50)(.65) + 50

Solve that for P....you should get your stated answer of $175.

Now, when P > $175, your order should cost LESS at company B....

 

[Math_Mark]

Thanks guys. I think I finally got it squared away.

X(.25) for Comp A

(X-50)(.35) for Comp B

After simplifying and reordering etc, I end up at .25x = .35x - 17.5

Then I solved for X and got 175.