5. A sign engraver makes signs with letters. He engraves identical letters in the same amount of time, and different letters possibly in different times. For two signs “ДОМ МОДЫ” and “ВХОД” together, he spent 50 minutes, and one sign “В ДЫМОХОД” he made in 35 minutes. How long will it take him to make the sign “ВЫХОД”?
Answer: 20 minutes.

## Solution.

In the signs FASHION HOUSE ENTRANCE and IN CHIMNEY, we separate the letters that form the word EXIT, then from the first sign, D, O, M, M, O, D will remain, and from the second - D, M, O. Note that FASHION HOUSE ENTRANCE differs from IN CHIMNEY by the letters D, O, M, and in time - by 15 minutes (50-35=15). Therefore, it takes 15 minutes to manufacture the letters D, O, M.

Now we know that when manufacturing IN CHIMNEY, 15 minutes were spent on manufacturing the letters D, M, O, i.e., the remaining 35-15=20 minutes were needed to manufacture the letters V, Y, X, O, D.

## Grading Criteria.

- Correct solution - 7 points.
- Time required for engraving the letters D, O, M found - 2 points.
- Arithmetic error in performing calculations - minus 1 point.