Jim is wrong here.
"Adequate amount" and "adequate amounts" would both be correct in this context. It is perfectly correct to talk about the "adequate amount of calcium needed for growing children," even though "children" is plural. The discrepancy - if one even exists - is that "amount" might refer to a single, agreed upon amount: exactly 8 hrs per person, per night, for example. "Amounts" might suggest that the amount of sleep might vary by person or by night.
This is what we call a RED HERRING split - intended to distract us, but not making a meaningful distinction between answer choices.
As Rich mentioned, the first 3 answer choices can be eliminated because the initial modifying phrase incorrectly modifies "people's." In E, in addition to the redundancy of "also," "the adequate amount they need" is also redundant. Thus, we're left with D.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education