a certain food contains 8 units per ounce of vitamin B1 and 12 units per ounce of Vitamin c. A second food contains 12 and 14 units per ounce of vitamins R1 an C, respectively. How many ounces of each are required for a meal that will contain 100 units of vitamin B` and 120 units of vitamin c?

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a certain food contains 8 units per ounce of vitamin B1 and 12 units per ounce of Vitamin c. A second food contains 12 and 14 units per ounce of vitamins R1 an C, respectively. How many ounces of each are required for a meal that will contain 100 units of vitamin B` and 120 units of vitamin c?

MIT 18.06 Linear Algebra, Spring 2010
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Let x & y be the ounces of each types of food required. Then total units of vit B1 & C obtained are 8x+12y and 12x+14y resp. Equating them with the vitamin requirement, we have: \[8x+12y=100 ; 12x+14y=120\] Solving them we get x=1.25 and y=7.5

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