Question

Cole needs to include at least 11 mg and at most 22 mg of iron in his diet each day. Cole plans to eat multiple bananas daily, and each banana has 0.3 mg of iron. Cole will get the rest of his iron from vitamins. Each whole vitamin contains 1 mg of iron. Part A If Cole eats 3 bananas each day, what is the least number of whole vitamins he must take in order to stay within his daily iron requirement? What is the greatest number of whole vitamins he can take in order to stay within his daily iron requirement? Use inequalities to solve. Respond in the space provided.

Answer 1

Let x be the number of vitamins Cole takes in a day. Since he eats 3 bananas each day and they represent 0.3 mg of iron, the total ammount of iron the bananas represent is 0.9 mg.

This is going to be complemented by the vitamins he takes, since each vitamin has 1 mg of iron, the total ammount of iron he takes in a day is:

`x+0.9`

We know that he has to take at least 11 mg and at most 22 mg of iron each day, then, the total ammount of iron he takes and is permitted can be express as:

`11\leq x+0.9\leq22`

Solving for x, we have:

`\begin{gathered} 11\leq x+0.9\leq22 \\ 11-0.9\leq x\leq22-0.9 \\ 10.1\leq x\leq21.91 \end{gathered}`

Therefore, Cole has to take at least 11 vitamins and at most 21 vitamins per day.