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.

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.

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