Ch 3 Percents

Question 1

What is the following as decimal?

Answer 1

Converting percents to decimals, move the decimal 2 places to the left. Think of FDP. You are going from P to D so move decimal 2 places to the left.

525% =  5.25
52.5% = .525
5.25%= .0525
.525% = .00525

Question 2

What is the following as percent?

Answer 2

Converting a decimal to percent, move the decimal 2 places to the right. Think of FDP. You are going from D to P, so move 2 decimal places to the right.

.6= 60%
.28= 28%
.459= 45.9%
1.3 = 1.30%

** Remember, percent is always bigger than decimal!

Question 3

What number is 50% greater than 60?

Answer 3

50% greater is the same as 150% therefore the question can be rephrased as what is 150% of 60?

Method 1) 1.5*60= 90 (best method to save time)
Method 2) 150/100=x/60= 90

Question 4

If the price of a $30 shirt is decreased by 20%, what is the final price of the shirt?

Answer 4

The question is asking for the new price therefore use the new percent/new value formula:

New Percent/value = New Value/Original Value
100%-20%= 80% (price after 20% decrease in price of shirt)

80/100=x/30
4/5=x/30
4/1=x/6 (remember to cancel out #’s always cancel vertically or horizontally but never diagonally when there is a ratio)
x=24

** Note, you could have found 20% of 30 and subtracted it from the original price of shirt but that includes extra step. To avoid waste of time and extra steps, set up ratio equation like above.

** % change can always be rephrased as a percent of the original, and a % of the original can always be rephrased as a percent change.

Question 5

If a ticket increased in price by 20% and then increased again by 5%, by what percent did the ticket price increase in total? Original cost of ticket is $100

Answer 5

Successive Interest Problem -
120/100*105/100*100
6/5* 21/20*100
6/5*21*5
6*21= 126

Question 6

A bank account with $200 earns 5% annual interest, compounded annually. If there are no deposits or withdrawals, how much money will the account have after 2 yrs?

Answer 6

Successive Interest Problem-
200*105/100*105/100
200* 21/20*21/20
21*21/2
= 220.50

Question 7

A bank account with $100 earns 8% annual interest, compounded quarterly. If there are no deposits or withdrawals, how much money will be in the account after 6 months?

Answer 7

**8% annual interest compounded quarterly means that 2% interest will be compounded per quarter. (8 annual int rate/4 quarters = 2 % int rate per quarter). Since the question is asking for account balance after 6 months, we only need to compute 2 quarters.

100102/100102/100= 102/100*102= 10404/100=104.04

Question 8

If 1,500 is increased by 20%, and than reduced by y%, yielding 1,080, what is Y?

Answer 8

Successive Interest Problem
If 1,500 is increased by 20%, then decreased by y%, then 1,080 is 120% of (100-y)% of 1,500

1,080=120/100* (100-y)/100*1500
1,080= 6/5( 100-y) 15
1,080= 6(100-y)3
1,080= 18(100-y)
60=100-y
y=40

** Be sure to write (100-y) in your original equation and not just y because equation is reduced by y%

Question 9

A bowl is half full of water. Four cups of water are then added to the bowl, filing the bowl to 70% of its capacity. How many cups of water are now in the bowl?

Answer 9

Method 1) Since the bowl was 50% full originally, adding 4 cups to water makes the bowl 70% of full capacity. Therefore, water increased by 20% of the total capacity

Use the Percent change formula since the percent changed from 50% to 70%.
Percent change= change in value/original value
20/100=4 cups/x
1/5=4/x
x=20

So bowl’s full capacity is 20 cups but the question is asking the number of cups currently in the bowl. So we need to find, what is 70% of 20.

x=70/100*20
x=14

Method 2) Save time by solving directly for 70% rather than by first solving for the full capacity. 4 represents 20% of the capacity. let x represent 70% of the capacity. Set up proportion and solve for x:

4/x=20/70
4/x=2/7
x=14

Question 10

A bottle is 80% full. The liquid in the bottle consist of 60% guava juice and 40% pineapple juice. The remainder of the bottle if then filled with 200ml of rum. How much guava juice is in the bottle.

Answer 10

If the bottle was 80% full and adding 200ml of the rum made the bottle full, then 200 ml is equal to 20% of the total capacity of the bottle. b= goal capacity of the bottle.

200=20/100b
1000=b ( bottle has total capacity of 1000 ml)

Now use successive percent to determine amount if guava juice.
G= 60/100* 80/100*1,000ml
G= 480 ml

** There was no use of the info given about pineapple

Question 11

A dress is marked up to 16(2/3)% to a final price of $140. What is the original price of the dress?

Answer 11

** Mark up is the same concept as % inc. so 16(2/3)% is the same as 116(2/3)%

**Convert the % to fraction. So 116(2/3)% is 116(2/3)/100/1= 350/3*1/100= 7/6

Original price of shirt= x
Mark up=7/6
Final price= 140

x(7/6)=140
x=1406/7
x=206
x=120

Question 12

What is the formula for change in percent/ change in actual value?

Answer 12

Original + Change= New

• • This equation is true for not only the percents but also actual amounts.
• • Original percent is always 100%

**Percent change/Change in actual value
=Change in Value/Original Value

Percent change/change in actual value= Absolute value of New Value-Old Value/Old value * 100

Question 13

What is the formula for new % or the new value?

Answer 13

New Percent = New Value/Original Value