Answer:
84/100
Step by step explanation:
Let's assume that the firm produces a total of 100 articles, then:
Four fifths of the articles are for export: 4/5 x 100 = 80 articles for export
The rest, or 1/5 of the articles, are for the domestic market: 1/5 x 100 = 20 articles for the domestic market
Of these 20 articles for the domestic market:
2/3 are guaranteed to one merchant: 2/3 x 20 = 40/3 = 13.33 articles guaranteed to one merchant (rounding to two decimal places)
1/9 are guaranteed to another merchant: 1/9 x 20 = 20/9 = 2.22 articles guaranteed to another merchant (rounding to two decimal places)
The total number of articles guaranteed to merchants is therefore 13.33 + 2.22 = 15.55.
The fraction of articles produced that goes on the open market is the remaining fraction after subtracting the articles guaranteed to merchants from the total production:
Total production = 100 articles
Articles guaranteed to merchants = 15.55 articles
Articles on the open market = 100 - 15.55 = 84.45 articles
Therefore, the fraction of the total articles produced that goes on the open market is:
84.45/100 = 0.8445, or approximately 84/100.