# Write a system of linear equations in three or four variables to solve exercises 47

Write a system of linear equations in three or four variables to solve exercises 47-48.

47. Three foods have the following nutritional content per ounce.

Calories Protein Vitamin C

Food a 40 5 30

Food B 200 2 10

Food C 400 4 300

If a meal consisting of the three foods allows exactly 660 calories,25 grams of protein and 425 milligrams of vitamin c, how many ounces of each kind of food should be used?

48. A furniture company produces three types of desks, a children model, an office model, and a deluxe model.

Each desk is manufactured in three stages: cutting, construction, and finishing. The time requirements for each model and manufacturing stage are given in the following table.

Children Model Office Model Deluxe Model

Cutting 2hr 3hr 2hr

Construction 2hr 1hr 3hr

Finishing 1hr 1hr 2hr

each week the company has available a maximum of 100 hours for cutting,100 hours for construction and 65 hours for finishing. If all available time must be used, how many type of desk should produce each week?

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