1. Look at the ten thousand won bill on the bottom right. Look at the picture on the right of the picture. Whose picture is this? It's the picture of King Se-jong.

2. How many minutes a day do teenagers watch TV? 179 minutes.

a. One hundred and seventy-nine minutes.
b. One hundred seventy-nine minutes.

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Are the explanation, question and answers are all correct?
Which answer is right, a or b? Are both correct?

Your first answer is correct.

The correct way of writing 179 minutes is one hundred seventy-nine minutes. Although informally, a. is also correct, it's better to leave out the "and" because it could be confused with a decimal point.

The explanation and question are correct. However, both answers a and b are correct as well. The difference between the two answers lies in the formatting of the number "179." Both ways of expressing the number are commonly accepted and understood, so either answer would be considered correct.