Question

The daily recommended serving of protein is $50$ grams. A nutritional store contains $32\%$ of the daily recommended serving of protein and $10\%$ of the daily recommended serving of fat. If the nutritional store contains $700\%$ more grams of protein than grams of fat, find the daily recommended serving fat (in grams).

• A. 20
• B. 15
• C. 12
• D. 27

Answer 1

Answer: (A)

20

First, determine the grams of protein in the bar.

If the bar contains $32\%$ of the daily recommended serving of protein and the daily recommended serving of protein is $50$ grams, then the bar contains $0.32\times 50=16$ grams of protein.

Next, determine the grams of fat in the bar by using the percent change equation: percent change $=$ $\frac{difference}{original}\times 100$.

The percent change is $700$, and the original is the grams of fat (because percent more means the original is the smaller number), which means $700=\frac{16-x}{x}\times 100$.

Divide both sides by $100$: $7=\frac{16-x}{x}$.

Multiply both sides by $x$ to get $7x=16-x$.

Add $x$ to both sides to get $8x=16$.

Divide both sides by $8$ and you find $x=2$.

That is the number of grams of fat in the bar.

To find the daily recommended serving of fat, translate English to math. $2$ is $10\%$ of the daily recommended serving, so if the daily recommended serving is $y$, $2=0.10y$.

Divide both sides by $0.10$ and you find that the daily recommended serving of fat is $20$.