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A Buy To Be Mathematical...

**What was needed to buy?**
**L**et's recollect the data where cost of each kind of wine bottle is listed.
- The cost of **1 French** wine bottle: **500$**

- The cost of **1 German** wine bottle: **100$**

- The cost of **20 Dutch** wine bottles: **100$ **(Cost of 1 bottle = 5$)

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Now let **F** be the number of **French** bottle, **G** be the number of **German **bottles and** D** be the number of **Du****tch** bottle that Simpson should buy.
F + G + D = 100
**G = 100 - F - D .....(1)**
Total cost of all bottle must be $10000.
500F + 100G + 5D = 10000
Substituting** (1****) **in above,
500F + 100(100 - F - D) + 5D = 10000
500F + 10000 - 100F - 100D + 5D = 10000
400F - 95D = 0
400F = 95D
80F = 19D
**D/F = 80/19**
Possible values of D and F are 80 and 19 respectively.
From (1),
**G = 100 - 19 - 80 = 1.**
Let's verify if all these fits in his budget or not.
19 French wine bottles would cost 19 x 500 = 9500, 1 German wine would cost = 1 x 100 = 100 and 80 Dutch wine bottles would cost 80 x 5 = 400. Remember we have got number of Dutch bottles in multiple of 20. Hence total cost = 9500 + 100 + 400 = 10000.
Hence with $10000, Simpson should buy **19 French**, **1 Ger****man** and **80 Dutch** wine bottles if conditions of buying 100 bottles & Dutch bottles in multiple of 20 are applied.
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