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.
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