USING MULTIPLE PERCENTAGES

About "Using multiple percentages"

Using multiple percentages :

Some situations require applying more than one percent to a problem.

For example, when we dine at a restaurant, we might pay a tax on the meal, and pay a tip to the wait staff.

The tip is usually paid on the amount before tax. When we pay tax on a sale item, we pay tax only on the discounted price.

Using multiple percentages - Examples

Example 1 : 

The Sanchez family goes out for dinner, and the price of the meal is $60. The sales tax on the meal is 7%, and they also want to leave a 15% tip. What is the total cost of the meal ?

Solution : 

Analyze Information : 

Identify the important information.

• The bill for the meal is $60.

• The sales tax is 7%, or 0.07.

• The tip is 15%, or 0.15.

The total cost will be the sum of the bill for the meal, the sales tax, and the tip.

Formulate a Plan : 

Calculate the sales tax separately, then calculate the tip, and then add the products to the bill for the meal to find the total.

Solve :

Sales tax : 0.07 × $60 = $4.20

Tip: 0.15 × $60 = $9.00

Meal + Sales tax + Tip  =  Total cost

$60 + $4.20 + $9  =  $73.20

Hence, the total cost is $73.20.

Justify and Evaluate : 

Estimate the sales tax and tip. Sales tax is about 10% plus 15% for tip gives 25%.

Find 25% of the bill : 0.25 × $60 = $15.

Add this to the bill : $60 + $15 = $75.

The total cost should be about $75.

The answers is close to the estimate, so the answer is reasonable.

Example 2 : 

Kedar earns a monthly salary of $2,200 plus a 3.75% commission on the amount of his sales at a men’s clothing store. One month he sold $4,500 in clothing. What was his commission that month? How much did he earn in all? Show your work.

Solution : 

Analyze Information : 

Identify the important information.

• Kedar's monthly salary is $2200.

• Commission of his sales is 3.75%, or 0.0375.

• In a particular month, he made a sale of $4500

The total will be the sum of salary and commission on sales..

Formulate a Plan : 

Calculate the commission on sales. 

Solve :

Commission on sales : 0.0375 × $4500 = $168.75

Salary + Commission on sales  =  Total earning

$2200 + $168.75  =  $2368.75

Hence, the total earning is $2368.75.

Justify and Evaluate : 

Estimate the commission. Commission on sales is about 4%. 

Find 4% of sales : 0.04 × $4500  =  $180.

Add salary and commission : $2200 + $180  =  $2380.

The total earning of Kedar is $2380.

The answers is close to the estimate, so the answer is reasonable.

After having gone through the stuff given above, we hope that the students would have understood "Using multiple percentages". 

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