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.
Accepted Solution
A:
Answer:2 pills of brand X, 2 pills of brand Y and 3 pills of brand Z.Step-by-step explanation:Required Vitamin :Vitamin A ⇒ 22 unitVitamin D ⇒ 18 unitVitamin E ⇒ 11 unitUnits of A, D, E per brand :X 2 1 2Y 3 2 2Z 4 4 1Let 'u' units of X 'v' units of Y 'w' units of Z requiredThen, 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 = 32 pills of brand X, 2 pills of brand Y and 3 pills of brand Z.