Question

solve each percent problem.
the # = % of # or part = % · whole. the percent is in decimal form.

1. what is 28.5% of 96?
2. $55\frac{1}{4}\\%$ of what number is 0.221?
3. what percent of 50 is 41?
4. jack ran 12 miles last week. this week, he ran 17 miles. what percent did he gain?

calculate the simple interest earned.
i = p·r·t, where i is the interest, p is principal, r is the rate and t is the time in years.

1. $588 interest is earned on a $2800 investment at 3%. find the time of the investment.
2. you take out a $10,500 loan to buy a car at a rate of 4.25% for 5 years. what will be the total cost of the car?

convert as indicated.
to change a fraction to a percent first divide, then multiply by 100%. always reduce if possible.

1. change to a percent : 32/78
2. change to a fraction : $0.\overline{4}$

Explanation:

Problem 1: What is 28.5% of 96?

Step 1: Convert percentage to decimal

To convert 28.5% to a decimal, we divide by 100: \( 28.5\% = \frac{28.5}{100} = 0.285 \)

Step 2: Multiply decimal by the number

We need to find 28.5% of 96, so we multiply 0.285 by 96: \( 0.285 \times 96 \)
Calculating this: \( 0.285 \times 96 = 27.36 \)

Step 1: Convert mixed fraction percentage to decimal

First, convert \( 55\frac{1}{4}\% \) to a decimal. \( 55\frac{1}{4} = 55.25 \), so \( 55.25\% = \frac{55.25}{100} = 0.5525 \)

Step 2: Let the number be \( x \)

We know that \( 0.5525 \times x = 0.221 \). To find \( x \), we divide both sides by 0.5525: \( x = \frac{0.221}{0.5525} \)
Calculating this: \( x = 0.4 \)

Step 1: Let the percentage be \( p \)

We can write the equation as \( \frac{p}{100} \times 50 = 41 \)

Step 2: Solve for \( p \)

First, simplify the left side: \( 0.5p = 41 \). Then divide both sides by 0.5: \( p = \frac{41}{0.5} = 82 \)

Answer:

27.36

Problem 2: \( 55\frac{1}{4}\% \) of what number is 0.221?