System of Linear Equations

Number of Civil, Electrical, and Mechanical Engineers and Their Average Ages

In an organization there are CE’s, EE’s and ME’s. The sum of their ages is 2160; the average age is 36; the average age of CE’s and EE’s is 39; the average age of EE’s and ME’s is 32 and 8/11; the average age of the CE’s and ME’s is 36 and 2/3. If each CE had been 1 year older, each EE 6 years and each ME 7 years older, their average age would have been greater by 5 years. Find the number of CE, EE, and ME in the group and their average ages.

Nutrition: Amount of food A, B and C to Meet the Nutrient Requirements

A nutritionist in a hospital is arranging special diets that consist of a combination of three basic foods. It is important that the patients on this diet consume exactly 310 units of calcium, 190 units of iron, and 250 units of vitamin A each day. The amounts of these nutrients in one ounce food are given in the following table.

  Units Per Ounce
Calcium Iron Vitamin A
Food A 30 10 10
Food B 10 10 30
Food C 20 20 20


How many ounces each food must be used to satisfy the nutrient requirements exactly?

A.   6 ounces of Food A, 5 ounces of Food B and 3 ounces of Food C
B.   3 ounces of Food A, 5 ounces of Food B and 6 ounces of Food C
C.   6 ounces of Food A, 3 ounces of Food B and 5 ounces of Food C
D.   5 ounces of Food A, 3 ounces of Food B and 6 ounces of Food C


System of Equations

System of Linear Equations
The number of equations should be at least the number of unknowns in order to solve the variables. System of linear equations can be solved by several methods, the most common are the following,

1. Method of substitution
2. Elimination method
3. Cramer's rule

Many of the scientific calculators allowed in board examinations and class room exams are capable of solving system of linear equations of up to three unknowns.

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