Question

A person is ordered by doctor to take 22 units of vitamin A, 18 units of vitamin D, and 11 units of vitamin E each day. There are three brands of vitamin supplement available: brand X contains 2, 1, and 2 units, brand Y contains 3, 2, and 2 units and brand Z contains 4, 4, and 1 units of vitamin A, D, and E, respectively. How many pills of each brand will provide the required amounts of vitamin? ___ pills of brand X, ___ pills of brand Y and ___ pills of brand Z.

Answer 1

2 pills of brand X, 2 pills of brand Y and 3 pills of brand Z.

Explanation:

Required Vitamin :

Vitamin A ⇒ 22 unit

Vitamin D ⇒ 18 unit

Vitamin E ⇒ 11 unit

Units of A, D, E per brand :

X 2 1 2

Y 3 2 2

Z 4 4 1

Let 'u' units of X

'v' units of Y

'w' units of Z required

Then,

2u + 3v + 4w = 22 ------(1)

1u + 2v + 4w = 18 ------(2)

2u + 2v + 1w = 11 -------(3)

By solving the linear equation

u = 2, v = 2, w = 3

2 pills of brand X, 2 pills of brand Y and 3 pills of brand Z.