Question

There are three types of foods,Food 1, Food 2 and Food 3. Food
Food I contains I unit of each of the nutrients A, B and

C. Food II contains I unit of nutrient A, 2 units of nutrient:
B and 3 units of nutrient C. Food III contains 1, 3 and 4
units of nutrients A, B and C respectively. 7 units of A, 16

units of B and 22 units of nutrient C are required. Find the
units of three foods that will provide exactly these amounts.
Use matrix method.

Answer 1

Given that,

There are three types of foods, Food 1, Food 2 and Food 3.

Let the nutrient in A, B and C is X, Y and Z

Food 1 :

A=X unit, B= Y unit, C = Z unit

Required nutrient of A = 7

Food 2 :

A=X unit, B= 2Y unit, C = 3Z unit

Required nutrient of A = 16

Food 3 :

A=X unit, B= 3Y unit, C = 4Z unit

Required nutrient of A = 22

We need to calculate the unit of three foods that will provide exactly amounts  

According to given data,

$X+Y+Z=7$.....(I)

$X+2Y+3Z=16$.....(II)

$X+3Y+4Z=22$....(III)

On subtracting equation (II) from equation (III)

$Y+Z=6$.....(IV)

Now put the value of Y+Z in equation (I)

$X+6=7$

$X=1$

Put the value of X in equation (II)

$1+2Y+3Z=16$

$2Y+3Z=15$...(V)

From equation (IV) and (V)

$Z=3$

Put the value of Z in equation (IV)

$Y=6-3$

$Y=3$

Hence, The unit of three foods that will provide exactly amounts are

In A,

Food I = 1 unit, Food 2 =3 unit, Food 2 =3 unit

In B,

Food I = 1 unit, Food 2 =6 unit, Food 3 = 9 unit

In C,

Food I = 1 unit, Food 2 =9 unit, Food 3 = 12 unit

Answer 2

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The unit of three foods that will provide exactly amounts are

In A

• Food I = 1 unit, Food 2 =3 unit, Food 2 =3 unit

In B

• Food I = 1 unit, Food 2 =6 unit, Food 3 = 9 unit

In C

• Food I = 1 unit, Food 2 =9 unit, Food 3 = 12 unit