30 PTS!!!!! 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 ba

Question

2 years ago

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30 PTS!!!!! 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 ba

nanas daily, and each banana has 0.3 mg of iron. Cole will get the rest of his iron from vitamins. Each whole vitamin contains 4 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.

Part B:
Cole continues to eat 3 bananas each day. He pays $2 for every 3 bananas he buys. His first 10 vitamins are free, but if he purchases more than 10 vitamins in 1 week, he pays an additional dollar for every 2 additional vitamins he purchases.

-Write an equation to describe the total amount of money Cole spends on bananas and vitamins each week.
-If Cole spends a total of $20 on bananas and vitamins this week and he takes the same number of whole vitamins each day, will he be able to meet his iron requirement every day this week, based on your answer in Part A?

Mathematics

2 answers:

ser-zykov [4K] · Answer 1 · 2023-09-14T14:20:45+03:00

Answer:

See explanation

Step-by-step explanation:

<u>Part A:</u> If Cole eats 3 bananas each day. These 3 bananas contain $3\cdot 0.3=0.9$ mg of iron.

Let x be the number of vitamins Cole takes. Each whole vitamin contains 4 mg of iron, then x vitamins contain 4x mg of iron.

The total amount of iron Cole takes is

$0.9+4x\ mg$

Cole needs to include at least 11 mg and at most 22 mg of iron in his diet each day, so

$11\le 0.9+4x\le 22$

Solve it:

$11-0.9\le 4x\le 22-0.9\\ \\10.1\le 4x\le 21.1\\ \\2.525\le x\le 5.275$

The smallest number of vitamins - 3, the greatest number of vitamins - 5.

<u>Part B: </u>Cole continues to eat 3 bananas each day. He pays $\$2\cdot 7=\$14$ for bananas per week.

If Cole spends a total of $20 on bananas and vitamins this week, then he spent $20 - $14 = $6 on vitamins.

Let x be the number of vitamins Cole takes this week.

First 10 vitamins are free, then x - 10 vitamins each cost $0.50 (he pays an additional dollar for every 2 additional vitamins he purchases) and they cost

$\$0.50(x-10)$

This amount of money is exactly $6, so

$0.50(x-10)=6\\ \\5(x-10)=60\\ \\x-10=12\\ \\x=22$

This means Cole takes 3 vitamins per day (the whole number) and he is able to meet his iron requirement every day this week, based on answer in Part A.