Basics
Q#1: This is 8.5% as a decimal.
What is 0.085?
We can divide a percent by 100 to get its decimal form.
8.5 divided by 100 gives us 0.085
Q#6: This is 3560 after a 25% increase.
What is 4450?
METHOD 1: 3560 + 0.25 * 3560 = 3560 + 890 = 4450
METHOD 2: 100% + 25% = 125% = 1.25
1.25 * 4450 = 4450
Q#11: The difference between interest and total.
What is interest is how much is earned from the borrower and total is the interest added to the principal amount?
Q#16: Based on your notes from yesterday, this is what we must do to before we can properly compare two deals.
What is we must make sure that one of the units is equivalent before we can properly compare the deals (i.e. unit rate)?
Q#21: This 22-year old American poet spoke at Biden's inauguration.
Who is Amanda Gorman?
Q#2: The sales price of a hoodie if its original price is $60 and it's on a sale for 25% off.
What is $45?
METHOD 1: 60 - 0.25 * 60 = 60 - 15 = $45
METHOD 2: 60 * 0.75 = $45
Q#7: This is 16% off of 90.
What is 75.6?
METHOD 1: 90 - 0.16 * 90= 90 - 14.4 = 75.6
METHOD 2: 100% - 16% = 84% = 0.84
0.84 * 90 = 75.6
Q#12: The interest Timothy makes in 3 months if he deposits $200 in his investment account with a 4% simple interest rate per month, assuming no deposits and withdrawals.
What is $24?
200 * 0.04 = $8 per month
8 * 3 = $24 Interest
Q#17: This is 40 after a 25% increase followed by a 10% decrease on that number (after the percent increase).
What is 45?
METHOD 1: 40 + 0.25 * 40 = 40 + 10= 50
50 - 0.10 * 50 = 50 - 5 = 45
METHOD 2: 40 * 1.25 * 0.9 = 45
Q#22: The words from this list that represents a percent increase.
1. Markdown
2. Markup
3. Discount
4. Tax
5. Percent Off
6. Tip
What are Markup, Tax, and Tip?
All of these will increase the original amount.
Q#3: The final total, if the cost of all your groceries is $55 and tax is 5%.
What is $57.75?
METHOD 1: 55 + 0.05 * 55 = 55 + 2.75 = $57.75
METHOD 2: 55 * 1.05 = $57.75
Q#8: The percent increase if there were 20 books on your shelf last week and there are 24 books on your shelf this week.
What is a 20% increase?
24 - 20 = 4 -> What percent is 4 out of the original?
4/20 = 0.2 -> 20 increased by 20% of itself to get to 24.
20 100%
24 120%
There was a 20% increase.
Q#13: The total amount of money in an account if the initial amount (principal) was $40, the simple interest rate is 3.5% per year, and the money is held there for 5 years without withdrawals or deposits.
What is $47?
40 * 0.035 = $1.40 interest per year
$1.40 * 5 = $7 interest in 5 years
Total = 40 + 7 = $47
Q#18: The amount of money that Tonya has if Kristin has $30, George has 20% more than Kristin, and Tonya has 30% less than George.
What is $25.20?
30 * 1.2 = $36
36 * 0.7 = $25.20
Q#23: The better deal of the two and why.
Deal A: 20 eggs for $10
Deal B: 25 eggs for $15
What is Deal A since it costs less money for 1 egg (you save 10 cents per egg)?
Deal A: 20 eggs for $10 -> 1 egg for $0.50
Deal B: 25 eggs for $15 -> 1 egg for $0.60
In Deal A, it costs less per egg. We can only compare deals if the units are the same.
Q#4: The two expressions that represent x after a markup (percent increase) of 35%.
What are x + 0.35x and 1.35x?
We add 35% of x back to x, or we find 135% of x.
Q#9: The percent increase in coyote population from last year to this year if there were 270 coyotes last year and there are 486 coyotes this year.
What is an 80% increase?
486 - 270 = 216 -> What percent is 216 out of the original?
216/270 = 0.8 -> 270 increased by 80% of itself to get to 486
270 is 100%
486 is 180%
There is a 80% increase.
Q#14: The total amount of money in an account if the initial amount (principal) was $60, the simple interest rate is 7.5% per year, and the money is held there for 3 years without withdrawals or deposits.
What is $73.50?
0.075 * 60 = $4.50 per year
$4.50 * 3 = $13.50 in 5 years
Total = 60 + 13.50 = $73.50
<<DAILY DOUBLE: Q#19>>
The better deal of the two and why.
Deal A: 20% off the total if you buy 5 pants for $8 each
Deal B: $2 off the total if you buy 4 pants for $6 each
What is Deal B because it costs less money per pants (you save 90 cents per pants)?
Deal A: 20% off of $40 -> $32 for 5 pants
1 pants = $6.40
Deal B: $2 off of $24 -> $22 for 4 pants
1 pants = $5.50
Q#24: The number of cups of orange juice in 6 containers if 3/4 of a container can hold 5 cups of orange juice.
What is 40 cups?
Containers Cups
0.75 5
6 ?
<<DAILY DOUBLE: Q#5>>
The TWO expressions below that represent a 45% increase of x.
A. 0.45x
B. 0.45 + x
C. 1.45x
D. x + 0.45x
E. 145x
What are C and D?
x + 0.45x is x being added to 45% of x
1.45x is 145% of x
<<DAILY DOUBLE: Q#10>>
The final price of a pair of sneakers if the original price is $120, there is a sale for 30% off the original price, and there is a sales tax of 8%.
What is $90.72?
0.3 * 120 = 36 -> 120 - 36 = 84
0.08 * 84 = 6.72 -> 84 + 6.72 = $90.72
120 * 0.7 * 1.08 = $90.72
Q#15: The number of years it will take Jules to earn $40 in interest if she initially deposited a principal of $100 in an account and there is a 5% simple interest rate, assuming she doesn't make any more deposits or withdrawals.
What is 8 years?
5% of 100 = 0.05 * 100 = $5 per year in interest
It will take Jules 8 years to make $40 since 8 * 5 gives us 40
Q#20: The percent increase from last month to this month, if there are 48 books in the second month and there were 25% fewer books in the first month than the second month.
What is a 33.3...% increase?
Method 1: 48 - 0.25 * 48 = 48 - 12 = 36 books in the first month
Method 2: 48 * 0.75 = 36 books in the first month
36 to 48 is a 33.3...% increase since 36 increases by 12 to get to 48
12/36 = 0.33... = 33.3...%
<<DAILY DOUBLE: Q#25>>
The total amount Jose paid for a bike if the original price of the bike was $200, he used a 40% discount coupon, and there was a sales tax of 5.5% applied after the discount.
What is $126.60?
METHOD 1: 40% decrease and a 5.5% increase
200 * 0.6 * 1.055 = $126.60
METHOD 2: 200 - 0.4 * 200 = 200 - 80 = 120
120 + 0.055 * 120 = 120 + 6.6 = $126.60