Business Mathematics: Ratio, Proportion, and Percent - Percent

The term percent, represented by the symbol %, is a mathematical term meaning one hundredth. Thus, for example, 50% = 50 hundredths = 50/100 = 0.50 and 37% = 37 hundredths = 37/100 =0.37.

Example 11
  (a)   Express 24% as a fraction and simplify:

  (b)   Express 7/20 as a percent:

To convert a percent to a decimal, simply drop the % symbol and move the decimal point two places to the left (divide by 100). If necessary, extra 0s can be inserted.

To convert a decimal to a percent, move the decimal point two places to the right (multiply by 100) and add the % symbol.

Example 12
(a)   Express 3.7% as a decimal:
3.7% = 0.037 (decimal point moved two places to the left; 0 is inserted to the left of the 3)

(b)   Express 0.375 as a percent:
0.375 = 37.5% (decimal point moved two places to the right, % symbol added)


Example 13
Express 3/8 as a percent.
First convert 3/8 to a decimal by division:

Then convert 0.375 to a percent by moving the decimal point two places to the right: 3/8 = 37.5%.
When the word of is used in connection with percents, it refers to multiplication. To solve problems, simply replace “of” by the symbol × and multiply.

Example 14
Compute 15% of 60:


Example 15
20% of what number is 40?
Let x = the number to be found. 20% of that number is 20% x = 0.20 × x:


Example 16
B&G Jewelry store is having a special sale. All ladies’ jewelry is 35% off. What is the saving on a lady’s ring which sells ordinarily for $350? What is the sale price?
35% of 350 = 0.35 × 350 = $122.50
The saving is $122.50. The sale price of the ring is $350.00 – $122.50 = $227.50.

Example 17
An art dealer buys a rare painting for $150,000 and resells it one year later for $175,500. Express her profit as a percentage of the original price paid for the painting.
Her profit is $175,500 – $150,000 = $25,500. The ratio of profit to the original price paid is 25,500/150,000 = 17/100 (divide by 1,500). Expressed as a percentage, her profit is 17%.

One common application of percents is the computation of sales tax. The amount of purchase is multiplied by the sales tax rate (usually expressed as a percent) to compute the tax to be collected. In other words,

Tax amount = Purchase price × tax rate

This equation can be expressed in two equivalent forms:


Example 18
How much tax will be collected on a purchase of $350 if the tax rate is 5%?


Example 19
There is an 8% tax on all purchases made in a certain Western city. How much of a purchase was made if the tax was $6.08?


Example 20
What is the tax rate if there is a tax of $42.50 on a $500 purchase?


Example 21
If there is a 6% sales tax on all purchases and a certain item purchased costs $795, what was the pretax price of the item purchased?
Since tax = 0.06 × price, it follows that price + 0.06 × price = 795. This is the same as 1.06 × price = 795. Divide by 1.06 to get price = 795/1.06 = $750.

Solved Problems

2.19   Express 36% as a fraction and simplify.
Solution


2.20   Express 3/5 as a percent.
Solution


2.21   (a)   Express 68.5% as a decimal.
(b)   Express 0.035 as a percent.
Solution
(a)   68.5% = 0.685 (move the decimal point 2 places to the left)
(b)   0.035 = 3.5% (move the decimal point 2 places to the right)

2.22   Express 5/16 as a percent.
Solution


2.23   Compute 32% of $120.
Solution
32% of 120 = 0.32 × 120 = 38.4. The amount of money is $38.40.

2.24 Because of a surplus in inventory, the price of light bulbs is being reduced from 40 cents to 32 cents apiece.
(a)  What percentage of the original price is the reduction?
(b)  What percentage of the sale price is the reduction?
Solution
The reduction is 8 cents.
(a)
(b)

2.25   How much tax will be collected on a purchase of a new automobile valued at $20,000 if the tax rate is %?
Solution


2.26   How much tax will be collected on a luxury item costing $12,750 if the rate is 7% on the first $10,000 and 10% on the amount over $10,000?
Solution
On the first $10,000:

On the amount over $10,000:


2.27   If the state sales tax is 6%, and a merchant charged $54.00 tax on a purchase, how much was the item purchased?
Solution


2.28 What is the local tax rate if tax of $4.95 is collected on a purchase of $90.00?
Solution