I’m not so good with word problems, for someone reason I always get confuse with the numbers and words and if I really need it or not. So here it is:
Jim Olsen makes and sells gourmet food items. He makes two types of salad dressings: garlic and tofu. Each gallon of garlic dressing requires 2 qt. of oil and 2 qt. vinegar. Each gallon of tofu dressing requires 3 qt. of oil and 1 qt of vinegar. Jim makes $3 profit on each gallon of garlic dressing and a $2 profit on each gallon of tofu dressing. He has 18 qt of oil and 10 qt of vinegar on hand. How many gallons of each type of dressing should he make to maximize his profits?
If you know a website that can help me that would be nice.
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3 Comments
Each gallon of garlic dressing needs 2 qts of oil and 2 qts of vinegar
Each gallon of tofu dressing needs 3 quarts of oil 1 qt of vinegar
Jim makes a profit of 3 dollars for every gallon of garlic dressing and 2 dollars for every gallon of tofu dressing.
One solution is to use 10 qts. of vinegar and 10 qts. of oil and make 5 gallons of garlic dressing. This will give 15 dollars. But he will be left with 8 qts. of oil and no vinegar.
Another solution is to make 6 gallons of tofu using 18 qts. of oil and 6 qts. of vinegar giving him 12 dollars profit and leaving him with 4 qts. of vinegar without oil.
This problem can be done as a linear equation and can be solved by graphical methods or by mathematical methods.
If a and b are the gallons of garlic and tofu dressings, we need
2a + 3b qts of oil and 2a + b qts. of vinegar
2a + 3b = 18
2a + b = 10
Subtracting the second equation from the first
2b = 8
b = 4
2a = 10 - b = 6
a = 3
So, Jim can make 3 gallons of garlic and 4 gallons of tofu to consume the total oil and vinegar. The profit made is 9 + 8 = 17 which is higher than the first two solutions that we saw above. Whether it is maximum needs to be seen graphically.
3 gallons of garlic and 4 gallons of tofu would turn the most profit: $17.00
to solve, i basically did the old “plug and chug” and tried to use all of the ingredients. 3 gallons of garlic is 6 quarts of both oil and vinegar which leaves 12 quarts of oil and 4 quarts of vinegar for the remaining 4 gallons of tofu.
I’m not very good w/ word problems either. But this web site is awesome http://www.webmath.com/
You enter the problem and it shows you how to do a problem and gives the correct answer. Good luck!