Exchanged 2214

In the table, the exchange rate list is an exchange office, but question marks replace some values. The exchange office exchanges money at the rates quoted and does not charge any other fees.

	nákup	prodej
1 EUR	26,20 CZK	28,00 CZK
1 GBP	b=? CZK	c=? CZK

1. How many euros (a =?) Will the customer receive it unless he exchanges CZK 4,200?

When a money changer buys £ 1,000 from a customer and then sells them all, his total profit is CZK 2,200. If, instead, the exchange sold 1,000 pounds and then exchanged all the torn crowns with another customer for pounds, he would earn 68.75 pounds.

2. For how many crowns does the exchange buy and sell 1 pound?

Correct answer:

a =  150 Eur
b =  32 CZK
c =  34.2 CZK

Step-by-step explanation:

$$\begin{gathered} a=4200/28 \\ 1000(c-b)=2200 \\ 1000(c-b)=68.75b \\ a=4200/28 \\ 1000\cdot (c-b)=2200 \\ 1000\cdot (c-b)=68.75\cdot b \\ 28a=4200 \\ 1000b-1000c=-2200 \\ 1068.75b-1000c=0 \\ Pivot:Row2\leftrightarrow Row3 \\ 28a=4200 \\ 1068.75b-1000c=0 \\ 1000b-1000c=-2200 \\ Row3-\frac{1000}{1068.75}\cdot Row2\to Row3 \\ 28a=4200 \\ 1068.75b-1000c=0 \\ -64.327c=-2200 \\ c=\frac{-2200}{-64.32748538}=34.2 \\ b=\frac{0+1000c}{1068.75}=\frac{0+1000\cdot 34.2}{1068.75}=32 \\ a=\frac{4200}{28}=150 \\ a=150 \\ b=32 \\ c=\frac{171}{5}=34.2 \end{gathered}$$

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