For in GOD we live, and move, and have our being.
- Acts 17:28
The Joy of a Teacher is the Success of his Students.
- Samuel Chukwuemeka
Calculator for Percents
For ACT Students
The ACT is a timed exam...$60$ questions for $60$ minutes
This implies that you have to solve each question in one minute.
Some questions will typically take less than a minute a solve.
Some questions will typically take more than a minute to solve.
The goal is to maximize your time. You use the time saved on those questions you
solved in less than a minute, to solve the questions that will take more than a minute.
So, you should try to solve each question correctly and timely.
So, it is not just solving a question correctly, but solving it correctly on time.
Please ensure you attempt all ACT questions.
There is no "negative" penalty for any wrong answer.
For JAMB and CMAT Students
Calculators are not allowed. So, the questions are solved in a way that does not require a calculator.
Solve all questions.
Use at least two methods (two or more methods) whenever applicable.
Show all work.
You may begin with a preview to ensure students understand it.
Preview is in black color.
Assume the cost of a phone is $\$200.00$
Include a $5\%$ sales tax
How much is the sales tax?
$
5\% = \dfrac{5}{100} = 0.05 \\[5ex]
5\%\:\:sales\:\:tax = 0.05(200) = \$10 \\[3ex]
Checkout\:\:price = \$200 + \$10 = \$210 \\[3ex]
$
Ask students this question:
Given: $\$210$, with $5\%$ sales tax (included), how can we get $\$10$?
In other words, Given the checkout price which includes the sales tax, how do we
figure out the sales tax?
Introduce and discuss the concept of Algebra (using variables).
First, we need to find the cost of the phone without the sales tax.
This is also known as the initial cost of the phone.
$
Let\:\:the\:\:initial\:\:cost\:\:of\:\:the\:\:phone = x \\[3ex]
5\%\:\:sales\:\:tax = 0.05(x) = 0.05x \\[3ex]
Initial\:\:cost + Sales\:\:tax = Checkout\:\:price \\[3ex]
x + 0.05x = 210 \\[3ex]
1.05x = 210 \\[3ex]
x = \dfrac{210}{1.05} \\[5ex]
x = 200 \\[3ex]
Sales\:\:tax = 0.05x = 0.05(200) = \$10 \\[3ex]
OR \\[3ex]
Sales\:\:tax = Checkout\:\:price - Initial\:\:cost \\[3ex]
Sales\:\:tax = 210 - 200 = \$10
$
You may begin with a preview to ensure students understand it.
Preview is in black color.
Assume the initial cost of a phone is $\$200.00$
Assume a $5\%$ discount (Assume it is on sale for $5\%$ off)
How much is the sale price?
$
5\% = \dfrac{5}{100} = 0.05 \\[5ex]
Discount = 5\%\:\:of\:\:200 = 0.05(200) = \$10 \\[3ex]
Sale\:\:price = 5\%\:\:off\:\:200 = \$200 - \$10 = \$190 \\[3ex]
Sale\:\:price = \$190 \\[3ex]
$
Ask students this question:
Given: $\$190$, with $5\%$ discount (included), how can we get $\$200$?
In other words, Given the sale price which includes the discount, how do we
figure out the actual price (initial price)?
Introduce and discuss the concept of Algebra (using variables).
$
Let\:\:the\:\:initial\:\:cost\:\:of\:\:the\:\:phone = x \\[3ex]
Discount = 5\%\:\:of\:\:x = 0.05(x) = 0.05x \\[3ex]
Sale\:\:price = 5\%\:\:off\:\:x = x - 0.05x = 0.95x \\[3ex]
Sale\:\:price = 190 \\[3ex]
\rightarrow 0.95x = 190 \\[3ex]
x = \dfrac{190}{0.95} \\[5ex]
x = 200 \\[3ex]
Initial\:\:price = \$200
$
You may begin with a preview to ensure students understand it.
Preview is in black color.
Assume the initial cost of a phone is $\$200.00$
Assume a $5\%$ discount (Assume it is on sale for $5\%$ off)
Include a $10\%$ sales tax
How much is the checkout price?
$
5\% = \dfrac{5}{100} = 0.05 \\[5ex]
Discount = 5\%\:\:of\:\:200 = 0.05(200) = \$10 \\[3ex]
Sale\:\:price = 5\%\:\:off\:\:200 = \$200 - \$10 = \$190 \\[3ex]
Sale\:\:price = \$190 \\[3ex]
10\% = \dfrac{10}{100} = 0.1 \\[5ex]
Tax = 10\%\:\:of\:\:190 = 0.1(190) = \$19 \\[3ex]
Checkout\:\:price = Sale\:\:price + Tax \\[3ex]
Checkout\:\:price = 190 + 19 = \$209 \\[3ex]
$
Ask students this question:
Given: $\$209$, with $5\%$ discount (included) and $10\%$ tax (included), how can we get $\$200$?
In other words, Given the checkout price which includes the discount and the tax, how do we
figure out the actual price (initial price)?
Introduce and discuss the concept of Algebra (using variables).
$
Let\:\:the\:\:initial\:\:cost\:\:of\:\:the\:\:phone = x \\[3ex]
Discount = 5\%\:\:of\:\:x = 0.05(x) = 0.05x \\[3ex]
Sale\:\:price = 5\%\:\:off\:\:x = x - 0.05x = 0.95x \\[3ex]
Tax = 10\%\:\:of\:\:0.95x = 0.1(0.95x) = 0.095x \\[3ex]
Checkout\:\:price = Sale\:\:price + Tax \\[3ex]
\rightarrow 209 = 0.95x + 0.095x \\[3ex]
209 = 1.045x \\[3ex]
1.045x = 209 \\[3ex]
x = \dfrac{209}{1.045} \\[5ex]
x = 200 \\[3ex]
Initial\:\:price = \$200
$
Title | Year of release | Length(minutes) |
---|---|---|
The Trouble with Harry | $1955$ | $99$ |
The Man Who Knew Too Much | $1956$ | $120$ |
The Wrong Man | $1956$ | $105$ |
Vertigo | $1958$ | $128$ |
North by Northwest | $1959$ | $136$ |
Psycho | $1960$ | $109$ |
The Birds | $1963$ | $119$ |
Marnie | $1964$ | $130$ |
Torn Curtin | $1966$ | $128$ |
Topaz | $1969$ | $143$ |
Frenzy | $1972$ | $?$ |
Family Plot | $1976$ | $?$ |
$M$ | $₦$ |
---|---|
$\dfrac{171}{1000}$ | $\dfrac{9}{40}$ |
$1$ | $p$ |
ACT
Use the following information to answer questions $31 - 33$
In $2012$, pollsters for the gallup Organization asked a random sample of $1,014$ adults.
"On the average, about how much does your family spend on food each week?"
The table below lists the percent of the sample that gave each response.
For example, approximately $21\%$ of adults in the sample responded that, on average, they spend no
less than $\$200$ but no more than $\$299$ on food each week.
Average amount spent | Percent of sample |
---|---|
Less than $\$50$ | $8\%$ |
$\$50$ to $\$99$ | $17\%$ |
$\$100$ to $\$124$ | $22\%$ |
$\$125$ to $\$149$ | $4\%$ |
$\$150$ to $\$199$ | $15\%$ |
$\$200$ to $\$299$ | $21\%$ |
$\$300$ or more | $10\%$ |
Did not give an amount | $3\%$ |
Paper | Percentage Obtained | Maximum Mark for Paper |
---|---|---|
$01$ | $55$ | $30$ |
$02$ | $60$ | $50$ |
$03$ | $80$ | $20$ |
Total | $\boldsymbol{100}$ |
Assessment | Weight | Your Score | Weighted Score |
---|---|---|---|
$01$ | $30$ | $55$ | $30 * 55 = 1650$ |
$02$ | $50$ | $60$ | $50 * 60 = 3000$ |
$03$ | $20$ | $80$ | $20 * 80 = 1600$ |
Student status | Approve | Disapprove | No opinion |
High school College Nonstudent |
$30$ $14$ $85$ |
$4$ $10$ $353$ |
$11$ $6$ $47$ |
Total | $129$ | $367$ | $64$ |
Type of shot | Number attempted | Percent successful |
---|---|---|
$1-point$ free throw $2-point$ field goal $3-point$ field goal |
$80$ $60$ $60$ |
$75\%$ $90\%$ $25\%$ |
Large animal | Number |
---|---|
Elephant Rhinoceros Lion Leopard Zebra Giraffe |
$600$ $100$ $200$ $300$ $400$ $800$ |
Total | $2,400$ |
Year | Price |
---|---|
$1$ $2$ $3$ $4$ $5$ |
$\$1.34$ $\$1.41$ $\$1.41$ $\$1.25$ $\$1.36$ |