## Task 2 - 200522

When making a purchase, the price of 170 Marks was paid with exactly 12 banknotes. Each of these banknotes was either a 10-Mark note or a 20-Mark note.

Determine the number of 10-Mark notes and the number of 20-Mark notes used to pay the specified amount!
The following table contains all combinations of 2 banknotes, each of which is either a 10-mark note or a 20-mark note. Subsequently, the total value is determined for each of these combinations:

| Number of notes of | Value of notes of |  |  |  |
| :---: | :---: | :---: | :---: | :---: |
| $10 \mathrm{M}$ | $20 \mathrm{M}$ | $10 \mathrm{M}$ | $20 \mathrm{M}$ | Total Value |
| 0 | 12 | $0 \mathrm{M}$ | $240 \mathrm{M}$ | $240 \mathrm{M}$ |
| 1 | 11 | $10 \mathrm{M}$ | $220 \mathrm{M}$ | $230 \mathrm{M}$ |
| 2 | 10 | $20 \mathrm{M}$ | $200 \mathrm{M}$ | $220 \mathrm{M}$ |
| 3 | 9 | $30 \mathrm{M}$ | $180 \mathrm{M}$ | $210 \mathrm{M}$ |
| 4 | 8 | $40 \mathrm{M}$ | $160 \mathrm{M}$ | $200 \mathrm{M}$ |
| 5 | 7 | $50 \mathrm{M}$ | $140 \mathrm{M}$ | $190 \mathrm{M}$ |
| 6 | 6 | $60 \mathrm{M}$ | $120 \mathrm{M}$ | $180 \mathrm{M}$ |
| 7 | 5 | $70 \mathrm{M}$ | $100 \mathrm{M}$ | $170 \mathrm{M}$ |
| 8 | 4 | $80 \mathrm{M}$ | $80 \mathrm{M}$ | $160 \mathrm{M}$ |
| 9 | 3 | $90 \mathrm{M}$ | $60 \mathrm{M}$ | $150 \mathrm{M}$ |
| 10 | 2 | $100 \mathrm{M}$ | $40 \mathrm{M}$ | $140 \mathrm{M}$ |
| 11 | 1 | $110 \mathrm{M}$ | $20 \mathrm{M}$ | $130 \mathrm{M}$ |
| 12 | 0 | $120 \mathrm{M}$ | $0 \mathrm{M}$ | $120 \mathrm{M}$ |

From this, it is evident that the total value of 170 marks is exactly achieved for the quantities 7 and 5 of 10-mark notes and 20-mark notes, respectively.