Question

The recommended daily allowance of magnesium for a college student is \(380 \mathrm{mg}\). If \(1 / 4\) cup of peanuts contains \(67 \mathrm{mg}\) of magnesium, how many cups of peanuts should a college student eat to get his or her daily intake of magnesium?

Short answer

Approximately 1.417 cups.

Step-by-step solution

– Identify Daily Requirement

The daily requirement of magnesium for a college student is given as 380 mg.

– Determine Magnesium per Serving

It is given that 1/4 cup of peanuts contains 67 mg of magnesium.

– Set Up the Equation

Let the number of cups of peanuts needed be represented by x. Since 1/4 cup contains 67 mg of magnesium, a full cup will contain 4 times that amount, which is 4 * 67 mg = 268 mg. The equation to find the number of cups (x) is: 380 mg = 268x.

– Solve for x

Solve the equation: x = 380 / 268 Calculate: x ≈ 1.417 cups.

– Check the Solution

Check the calculation by multiplying 1.417 cups by 268 mg/cup to confirm it is close to 380 mg.

Key concepts

recommended daily allowance

Understanding the recommended daily allowance (RDA) of a nutrient is essential for maintaining good health. The RDA is the amount of a nutrient needed to meet the requirements of nearly all (97-98%) healthy individuals in various age and gender groups. For magnesium, this value varies with age and gender, but for a college student, it is set at 380 mg. Meeting the RDA helps in ensuring that the body performs various vital functions effectively. Magnesium plays roles in muscle function, nerve function, and maintaining bone health.
Ignoring the RDA can lead to deficiencies or excesses, both of which can cause health issues. For instance, too little magnesium can result in muscle cramps and high blood pressure, while too much can cause diarrhea and abdominal pain.
Therefore, knowing the RDA and understanding how to fulfill it through diet is key to a healthy lifestyle.

nutritional calculations

Nutritional calculations are fundamental for proper dietary planning. In our exercise, we calculate the number of cups of peanuts needed to meet the magnesium RDA for a college student.
We start by noting that 1/4 cup of peanuts provides 67 mg of magnesium. To find the magnesium content in a full cup, we simply multiply this value by 4, resulting in 268 mg per cup.
Next, to determine how many cups of peanuts are needed, we set up a simple equation. If x represents the number of cups needed, we have:

• 268x = 380
• x = 380 / 268
  This division yields approximately 1.417 cups. This means that a college student requires a little more than 1.4 cups of peanuts to meet their daily magnesium requirement. Ensuring accurate nutritional calculations helps maintain a balanced diet and supports overall health.

unit conversion in chemistry

Unit conversion in chemistry is often necessary when dealing with nutritional values. In the given exercise, we converted the magnesium content from 1/4 cup measurements to full cup measurements. This required multiplication or division, essential tools in unit conversion.
For example, knowing that 1/4 cup of peanuts contains 67 mg of magnesium, we calculate the magnesium content in a full cup as follows:

• 1 cup = 4 * 1/4 cup
• Therefore, 1 cup = 4 * 67 mg
• 1 cup = 268 mg
  Understanding and performing these conversions is crucial in chemistry and diet planning. It allows for clear and accurate communication of measurements and aids in the precise formulation of dietary recommendations. Accurately converting units ensures that individuals meet their nutritional needs without over- or under-consuming any nutrient.