Astore sells forks for $3.50 each, spoons for $3.80 each, and knives for $4.25 each. ken wants to have a ratio of forks to spoons to knives of 5: 4: 2. he can spend a maximum of $300. what is the greatest number of forks ken can buy?

Forks to spoons to knives5:4:2added = 11so 5/11 of the total amount is spent on forks, 4/11 of the total amount is spent on spoons, and 2/11 of the total amount is spent on knives.

so if there is a total amount of 300 (maximum)
5/11 * 300 = 1500/11 = 136.36 is spent on forks 
4/11 * 300 = 1200/11 = 109.09 is spent on spoons
2/11 * 300 = 600/11 = 54.55 is spent on knives

so if $ 136.36 is what can be spent on forks, and forks cost $ 3.50 eachthen at most, he can get : 136.36 / 3.50 = 38.96 rounds to 38 forks <==