A store 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 knives ... 5:4:2 ... added = 11 ... so 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 each ... then at most, he can get : 136.36 / 3.50 = 38.96 rounds to 38 forks <==

5 x 3.50 = $17.50

4 x 3.80 = $15.20

2 x 4.25 = $8.50

17.50 + 15.20 + 8.50 = $41.20

Each bundle containing 5 forks, 4 spoons and 2 knives would cost him $41.20. To keep the ratio he would buy this "bundle" as many times as the $300 limit allowed, meaning you must divide 300 by 41.20

300/41.20 = 7.28

Fractions are irrelevant because it would mean not being able to buy some of the items, which would mess up the ratio. So 7 is the amount of times he can buy 5 forks, 4 sponsors and 2 knifes. So the amount of forks is:

7x5 = 35 forks