Solving for Percent, Part or Whole

Which of the following statements is false?

• Percent problems can be solved using proportions, which is a mathematical tool that helps you compare two ratios and find an unknown value.

• Proportions are the only way to solve percent problems.

Which proportion can you use to solve percent problems?

• whole/part = 100/percent

• whole = part × percent/100

• percent = whole/part × 100

• part/whole = percent/100

Answer explanation

In percent problems, proportions are a valuable tool used to compare two ratios and find an unknown value, such as the percent, part, or whole. The general structure of a proportion for percent problems is: part/whole = percent/100.

John runs a car wash business. In a single month, he earned $4,500 in car wash fees. After deducting all expenses, his profit for the month was $1,350. What percent of his sales for the month was profit?

• 30%

• 25%

• 35%

• 20%

Answer explanation

You can set up a proportion to find the percentage of John's sales that represents his profit.

Let "x" be the percentage of his sales that is profit.

The part-to-whole relationship can be expressed as:

Profit / Total Sales = x / 100

Now, let's substitute the known values into the proportion:

$1,350 / $4,500 = x / 100

Next, cross-multiply and divide by $4,500 to isolate "x":

x = ($1,350 × 100) / $4,500

x = 30

So, John's profit represents 30% of his sales for the month. 

 During a special promotion, a clothing store is offering a 20% discount on all items. If a customer purchases a dress that originally costs $120, how much money will the customer save with the discount?

• $30.00

• $20.00

• $24.00

• $96.00

Answer explanation

To find out how much money the customer will save with the discount, you can use a proportion to solve the problem.

Let "x" be the discount amount that the customer will save.

The part-to-whole relationship can be expressed as:

Discount Amount / Original Price = Percent / 100

Now, let's substitute the known values into the proportion:

x / $120 = 20 / 100

Next, cross-multiply and divide to solve for "x":

x = ($120 × 20) / 100

x = $2,400 / 100

x = $24.00

Therefore, the customer will save $24.00 with the 20% discount.

Samantha recently filed her income taxes and found that she paid $1,800 in taxes. The tax rate for her income bracket is 12%. What was Samantha's total income before taxes?

• $14,000

• $15,000

• $17,000

• $13,000

Answer explanation

To find Samantha's total income before taxes, you can use a proportion to solve the problem.

Let "x" be Samantha's income before taxes.

The part-to-whole relationship can be expressed as:

Tax Amount / Total Income = Tax Rate / 100

Now, let's substitute the known values into the proportion:

$1,800 / x = 12 / 100

Next, cross-multiply and divide to solve for "x":

$1,800 100 = 12 x

$180,000 = 12 * x

Now, isolate "x" by dividing both sides by 12:

x = ($1800 × 100) / 12

x = $180,000 / 12

x = $15,000

Therefore, Samantha's total income before taxes was $15,000.