A zookeeper wants to give an animal 42 mg of vitamin A and 65 mg of vitamin D per day.

Question

He has two supplements: the first contains $10\%$ vitamin A and $25\%$ vitamin D; the second contains $20\%$ vitamin A and $25\%$ vitamin D. How much of each supplement should he give the animal each day?

Let $x$ = vitamin A

Let $y$ = vitamin B

I began with the equations

$$\begin{align*}0.1x + 0.25x &= 42 \\ 0.2x + 0.25y &= 65 \end{align*}$$

I used row operations on a series of matrices to receive the solutions

$$\begin{align*}x &= 230 \\ y &= 190 \end{align*}$$

I just don't know how to phrase the conclusion.. do I say that the zookeeper needs $230$ mg of the first supplement and $190$ of the second supplement? From a biological perspective this seems too much but if I remember correctly excessive vitamins get washed out via urination. How would I properly phrase the conclusion?

Answer 1

Your system is wrong. Let $x$ denote the amount of the first supplement and $y$ the amount of the second supplement. Then the total amount of vitamin A is $0.1x + 0.2y$ and the total amount of vitman D is $0.25x + 0.25y$. This means your system of equations should be:

$$\begin{align*}0.1x + 0.2y &= 42 \\ 0.25x + 0.25y &= 65 \end{align*}$$

Now you need to solve this system correctly. The solution of this system is

$x = 100$ and $y = 160$. These amounts will lead to the animal getting exactly $42$ mg of vitamin A and $65$ mg of vitamin D.