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| 9 Theory slides |
| 9 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
Here are a few recommended readings before getting started with this lesson.
Vincenzo went out for dinner together with his family. The total cost of the meal was $124. Because they really enjoyed the food and the service, they left a 20% tip.
How much tip did they leave?
Interest is the cost of borrowing money from a bank or additional money earned from keeping money in a bank account. There are several types of interest, but only simple interest will be introduced in this lesson.
The interest that is applied only to an initial amount of money is called simple interest. The initial amount is known as the principal. Simple interest is calculated as a product of principal, annual interest rate, and the time in years.
Years | Amount of Simple Interest | Balance |
---|---|---|
1 | 1000⋅0.03⋅1=$30 | 1000+30=$1030 |
2 | 1000⋅0.03⋅2=$60 | 1000+60=$1060 |
3 | 1000⋅0.03⋅3=$90 | 1000+90=$1090 |
4 | 1000⋅0.03⋅4=$120 | 1000+120=$1120 |
5 | 1000⋅0.03⋅5=$150 | 1000+150=$1150 |
Vincenzo is a very thrifty child and saves some of his allowance every month. His father thinks that opening a savings account for Vincenzo's savings would be great for him. He wants to support Vincenzo and plans to deposit $5000 in this account as principal.
After talking with several bankers, he notices that banks offer different interest rates.
Substitute values
Write as a decimal
Multiply
Substitute values
Multiply
LHS/20000=RHS/20000
ba=b/100a/100
Write as a decimal
Convert to percent
Rearrange equation
Vincenzo goes to Miami, Florida, to visit his aunt and uncle. The city's sales tax rate is 7%. Vincenzo wants to buy a new coat. The price of the coat before tax is $120. Vincenzo says that the total cost can be calculated by finding 7% of $120 and adding this value to $120.
However, the salesperson says that to find the selling price, the price of the coat $120 needs to be multiplied by 1.07. Who is correct?Calculate the total cost using the methods described by Vincenzo and the salesperson. Use the percent equation to calculate the amount of the tax.
p=7, w=120
a%=100a
ca⋅b=ca⋅b
Calculate quotient
Write as a sum
Distribute 120
Multiply
Add terms
Vincenzo visits several more shopping centers in Miami. He buys a pair of sneakers and some jeans at a department store. Below is his receipt.
a=10.00, w=34.00
Rearrange equation
LHS/34.00=RHS/34.00
Use a calculator
Convert to percent
Round to nearest integer
a=44.00, p%=120%
a%=100a
ca⋅b=ca⋅b
LHS⋅100=RHS⋅100
LHS/120=RHS/120
Calculate quotient
Round to 2 decimal place(s)
Rearrange equation
Vincenzo's aunt signed an agreement when she joined a company two years ago. If she is still working with the company after two years, she will receive a bonus equivalent to 8% of the contract's total value.
If Vincenzo's aunt makes $1200 a month, how much money will she make as a bonus?Calculate the total amount of money that she earns in twenty-four months, then calculate 8% of that amount.
p=8, w=28800
a%=100a
ca⋅b=ca⋅b
Split into factors
Cancel out common factors
Simplify quotient
Multiply
Vincenzo's uncle borrows $2400 to repair his car. He will pay off the loan over 4 years by paying back the principal plus 3.5% simple interest for each year.
a%=100a
ca⋅b=ca⋅b
Multiply
Calculate quotient
Let's recall the definitions of given concepts so we can pair up the options. Let's start with the sales tax.
Sales tax is an amount charged by the government that the customer pays in addition to the selling price for some product or service.
This means that sales tax is an additional amount of money charged on items or services. Next, let's consider when we might give a tip. In restaurants, we often give extra money to the server voluntarily when we are satisfied with the service. This is called a tip.
A tip is an amount of money above the cost of an item or service that is given in appreciation of the service.
Generally speaking, a store sells items for more than it pays for those items. This is how the store makes a profit. This amount of increase is called the markup. In other words, the markup is difference between the selling price and the cost of the item to the store.
Markup is the amount of increase from what the store pays for an item to the selling price of that item to the customer.
Finally, the selling price of an item or service is the amount that the customer pays for that item or service. It is the final price of the item or service after adding any markups or subtracting any discounts.
The selling price is the amount of that the customer pays for an item or service.
Let's finally pair the concepts and their definitions in a table.
Concept | Definition |
---|---|
Sales Tax | An additional amount that is added to the price of an item by the government |
Tip | Money a customer gives a worker above the price in return for a service |
Markup | The amount of increase from what the store pays to what the customer pays |
Selling Price | The amount that the customer pays for an item |
Find the total cost of the given items.
We want to find the selling price of the laptop. Let's start by calculating the dollar amount of the tax. We can then add it to the retail price. Let's use the percent equation to find the amount of tax to be paid. part = percent * whole We are given that the price of the laptop is $ 980 and the tax is 4 %. Let p represent the dollar amount of the tax. Our equation then takes the following form. p = 4 % * $ 980 We can write the percent as a decimal before we solve the equation. We do this by ignoring the percent symbol and moving the decimal point two places to the left. 4 % ⇔ 0.04 Now we can do the multiplication. Let's ignore the units for now for simplicity.
We got that p= 39.20. This means that the amount of tax is $ 39.20. Now we can calculate the total cost of the laptop by adding this amount to $ 980. $980 + $ 39.20 = $ 1019.20 This means that the total cost of the laptop is $ 1019.20.
We can use the percent equation again to find the amount of the tip. After that, we will add the tip amount to the price of the dinner to find the final cost. part = percent * whole We know that the dinner is $32, which corresponds to the value of the whole, and that the tip, or the percent, is 15 % of the whole. Let's calculate the value of part by substituting these values into the equation. Remember to rewrite the percent as a decimal number.
Since a tip is an additional amount of money given in return for a service, we will add this amount to the price of the dinner. This will give the total amount of money paid for the dinner. $32 + $ 4.80 = $ 36.80 The total cost of the dinner is $36.80.
We will use the percent equation to find the original price of the cell phone. part = percent * whole We are given that a cell phone costs $ 820 when it is on sale for 30 % off. This means that the sale price is 100 % -30 %, or 70 %, of the original price. If we let p represent the original price, then we have the following equation. $ 820 = 70 % * p Let's write the percent as a decimal before we solve the equation. We can do this by ignoring the percent symbol and moving the decimal point two places to the left.
This means that 70 % is equal to 0.70 or 0.7. $ 820 = 70 % * p [0.3em] ⇓ [0.3em] $ 820 = 0.7 * p Finally, we will solve the equation for p. We can ignore the units for now for simplicity.
We found that the original price of the cell phone is about $ 1171.43.
We want to determine which of the given words increase the final amount of money to be paid. Let's recall the definitions of these terms.
Definition | Explanation | |
---|---|---|
Discount | A decrease in the usual price of something | Selling Price= Regular Price - Discount |
Markup | The amount of increase from what the store pays for an item to the price that the customer pays | Price=Cost to Store + Markup |
Tip | Money a customer gives a worker in appreciation in return for a service | Final Cost=Selling Price + Tip |
Tax | An amount charged by the government that the customer pays in addition to the price for some product or service | Selling Price=Regular Price + Tax |
Markdown | The amount by which the regular price of item is decreased | Selling Price=Regular Price - Markdown |
Gratuity | Money paid to a specific service worker to appreciate a job well-done | Final Price=Regular Price + Gratuity |
According to the table, we can say that markup, tip, gratuity, and tax represent an increase in the final amount of money to be paid, while discount and markdown reduce the price of an item or service.
If we borrow money from a bank, we pay the bank interest for the use of their money. We will use the simple interest formula to calculate the interest rate r that the bank charges on the loan given to Zosia's father. cl I= p r t, where & I =Interest & p& = Principal r& = Annual interest rate t& = Time (in years) We know that Zosia's father received a $5200 loan from the bank. He will pay $1300 interest over 5 years. I=1300 , p= 5200, t= 5 We want to calculate the annual interest rate r. Let's substitute these values into the simple interest formula and solve it for r.
The annual interest rate is 5 %.