### 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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