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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
We want to determine whether the trampoline is free after applying both discounts. We will do this by calculating the price of the trampoline after both discounts one at a time.
Let's find the sale price of the trampoline after the first 50 % discount. First, we will subtract 50 % from 100 % to find the percent that represent the sale price as a percent of the original price. 100 % - 50 %= 50 % The sale price is 50 % of the original price. Let's use the percent equation, which tells us that the part of the whole a is the percent p multiplied by the whole w. Here, the sale price is the part a, the percent is 50, and the whole w is the original price, 340 dollars.
The sale price of the trampoline after the first discount is $170.
Now we will calculate the sale price of the trampoline after the second 50 % discount. Let's use the percent equation once again. In this equation, the final sale price is the part a, the percent is still 50, and the whole w is the price after the first discount, 170 dollars.
As we can see, the final sale price of the trampoline after the second discount is $85. This means that the trampoline is not free.
Since the prompt asks whether or not the selling price will be zero, we can determine the answer by writing the percent discounts as fractions. Remember that when expressed as a fraction, the whole is 1. The original cost of the trampoline represents 100 % of the price and is also the whole. A 50 % discount represents 12 of that price. rcl 100 % & ⇔ & 1 [0.8em] 50 % & ⇔ & 1/2 Now let's calculate the first discount as a fraction. 1-1/2=1/2 After the first discount, the trampoline will cost half as much as the original price. The store offers another 50 % discount, so the price is lowered again by 12. In other words, the discounted price will be discounted again by half. Let's calculate half of the half as a fraction. 1/2 * 1/2=1/4 As we can see, the final selling price is a quarter of the original price. This means that the trampoline will not be free.