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Algebra
Pregunta

A dietician prescribes a special dietary plan using two different foods. Each ounce of food \(X\) contains \(180\) milligrams of calcium, \(6\) milligrams of iron, and \(220\) milligrams of magnesium. Each ounce of food \(Y\) contains \(100\) milligrams of calcium, \(1\) milligram of iron, and \(40\) milligrams of magnesium. The minimum daily requirements of the diet are \(1000\) milligrams of calcium, \(18\) milligrams of iron, and \(400\) milligrams of magnesium. 

(a) Write and graph a system of inequalities that describes the different amounts of food X and food \(Y\) that can be prescribed. 

(b) Find two solutions of the system and interpret their meanings in the context of the problem. 

A dietician prescribes a special dietary plan usin...

Answer

a)

180x + 100y > 1000

6x + y > 18

220x + 40y > 400

b)

 i) x = 4, y = 8

Consuming food X in quantity 4 ounces and  food Y in quantity 8 ounces, will fulfil the dietary requirements.

ii) x = 8, y = 6

Consuming food X in quantity 8 ounces and  food Y in quantity 6 ounces, will fulfil the dietary requirements.

Solución
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