### Brain Teasers

# Wash Cloths and Cleaner

A shopkeeper has two products, a wash cloth and a cleaning product.

The wash cloth sells at £0.32, and the cleaner at £0.74.

However, people buy lots of the wash cloths, but little of the cleaner. He wants to get rid of the cleaner by selling off all the remaining stock by bundling wash cloths with it.

He wants to keep the same profit margins as he would have originally.

If the average price for each item is £0.40, what is the smallest possible bundle, and what does it cost?

The wash cloth sells at £0.32, and the cleaner at £0.74.

However, people buy lots of the wash cloths, but little of the cleaner. He wants to get rid of the cleaner by selling off all the remaining stock by bundling wash cloths with it.

He wants to keep the same profit margins as he would have originally.

If the average price for each item is £0.40, what is the smallest possible bundle, and what does it cost?

### Answer

He bundles 17 wash cloths with 4 cleaners for £8.40.Let x = quantity of wash cloths

Let y = quantity of cleaners

(0.32x + 0.74y) / (x + y) = 0.40

0.32x + 0.74y = 0.40x + 0.40y

0.34y = 0.08x

0.17y = 0.04x

The smallest integers are: x = 17 wash clothes, y = 4 cleaners. The total cost is: 0.32(17) + 0.74(4) = 8.40. The average cost is 8.40 divided by 21 items, or 0.40.

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## Comments

Unfortunately your answer is flawed. If you add up the price of the original products the price should be 2.02. He would we be decreasing his profit margin by .02 per bundle or .004 per item (5 in the bundle). Here is a good way to solve this: Let X = the number of cloths and Y= the number of cleaners.

Then .32X + .74Y / X+Y = .40 Solving for Y: Y= 4/17 X. Now graphing this out you will see that the lowest point where X and Y are whole numbers is when X = 17 and Y = 4. Therefore 17 washcloths bundled with 4 cleaners would cost 8.40. That's 21 items with an average cost of .40.

Then .32X + .74Y / X+Y = .40 Solving for Y: Y= 4/17 X. Now graphing this out you will see that the lowest point where X and Y are whole numbers is when X = 17 and Y = 4. Therefore 17 washcloths bundled with 4 cleaners would cost 8.40. That's 21 items with an average cost of .40.

I'm very sorry you're right. I was playing about with the numbers during an idle moment, and thought I would do something that would be relatively easy. Sorry I must have made a silly mistake with the numbers!

By the way....it was very fun and I liked it a lot, so thanks.

Het Cathal, does this mean that by your own style of logic, That I proved you wrong? We must be told. I think this is how you did it.

Aug 24, 2002

Why is the puzzle still on the site if even the author admits it is wrong?

This person who post these brain teasers needs to stop. They usually give wrong answers, and admits to them. Don't post something if you don't know the answer.

Can't we remove blatantly wrong teasers?

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