Chapter A.9, Problem 120AYU

To determine

To find: For food products to be labeled “light,” the U.S. Food and Drug Administration requires that the altered product either must contain at least one-third fewer calories than the regular product or must contain at least one-half less fat than the regular product. If a serving of Miracle Whip® Light contains 20 calories and $1.5$ grams of fat, then what must be true about either the number of calories or the grams of fat in a serving of regular Miracle Whip®?

Answer to Problem 120AYU

The fat is true in a serving of regular Miracle Whip®.

Explanation of Solution

Given:

For food products to be labeled “light,” the U.S. Food and Drug Administration requires that the altered product either must contain at least one-third fewer calories than the regular product or must contain at least one-half less fat than the regular product. If a serving of Miracle Whip® Light contains 20 calories and $1.5$ grams of fat.

Calculation:

Let $x$ be the number of calories, and $y$ be the number of grams of fat in serving of the regular product.

Given that at least one-third fewer calories than the regular product or must contain at least one-half less fat than the regular product. We can write $20 \le \frac{1}{3}x$ or $1.5 \le \frac{1}{2}y$

In regular Miracle Whip® contains 40 calories and $3.5$ gram fat (Source from company website)

Therefore $x = 40$ and $y = 35$

Calories:

$20 \le \frac{1}{3}x = \frac{1}{3}\left(40\right) = 13.33$

Fat:

$1.5 \le \frac{1}{2}y = \frac{1}{2}\left(3.5\right) = 1.75$

Therefore the fat is true in a serving of regular Miracle Whip®.