Percents and ratios

Question 1

1/3

Answer 1

0.33333

Question 2

2/3

Answer 2

0.66666

Question 3

1/5

Answer 3

0.2

Question 4

2/5

Answer 4

0.4

Question 5

3/5

Answer 5

0.6

Question 6

4/5

Answer 6

0.8

Question 7

1/6

Answer 7

0.166666

Question 8

5/6

Answer 8

0.833333

Question 9

1/7

Answer 9

0. 14285714

0. 143

Question 10

1/8

Answer 10

0.125

Question 11

3/8

Answer 11

0.375

Question 12

5/8

Answer 12

0.625

Question 13

7/8

Answer 13

0.875

Question 14

1/9

Answer 14

0.111111

Question 15

An item initially cost $100. At the beginning of the year, the price increased 30%. After the increase, an employee purchased it with a 30% discount. What price did the employee pay?

Answer 15

30% increase = 1.3 (multiplier)
30% decrease = 0.7 (multiplier)
product of multipliers :
100 x 1.3 x 0.7 = $91

Question 16

At the beginning of the year, the price of an item increased 30%. After the increase, an employee purchased it with a 40% discount. The price the employee paid was what percent below the original price?

Answer 16

1.30 x 0.60 = 0.78
That’s the multiplier for a 22% decrease.
The price the employee paid was 22% below the original price

Question 17

The price of stock increased 20% in January, dropped 50% in February, and increased 40% in March. Find the percent change for the three-month period

Answer 17

1.20 x 0.5 x 1.4 = 1.20 x 0.7 = 0.84
That’s the multiplier for a 16% decrease
the stock decreased 16%

Question 18

Sheila invests $4000 in an account that yields 6% compounding annually for 8 years. What is the total amount after 8 years?

Answer 18

4000 x (1.06)^8

Question 19

Susan invests $1000 in an account that yields 5% annual, compounding quarterly, then how much does she have after 6 years?

Answer 19

Quarterly percent = 5/4 = 1.25%
Mutliplier = 1.0125
The amount in the account experiences that percent increase 4 times each year, or 24 times in six years
1000 x (1.0125)^24

(estimate : simple interest = $1300)

For any compounding period smaller than a year, we need n, where n is the number of times that compounding period would occur in a year
Quarterly, n = 4
Monthly, n = 12
Daily, n = 365
Suppose the bank pays 5% annual interest compounding quarterly : the bank would pay 5/4 = 1.25% each quarter
In general, if there are n compounding periods in the year, we divide the annual percent of interest by n to get the percent for each individual compounding period
Shorter (more) compounding periods = more overall amount of interest

Question 20

In a class, the ratio of boys to girls is 3:7. If there are 32 more girls than boys, how many boys are there?

Answer 20

boys = 3n
girls = 7n
7n - 3n = 4n = 32
n = 8
boys = 3n = 3 x 8 = 24

Question 21

boys to girls is 3:5. boys are what fraction of the whole?

Answer 21

3/8

Question 22

General-purpose concrete is created using a 1:2:3 ratio of cement to sand to gravel. If we have 150 kgs of sand available, how many kgs of concrete can we make? (assuming we have more than enough cement and gravel)

Answer 22

sand : concrete = 2:6 = 1:3
1/3 = 150/x
x = 3*150 = 450kgs of sand

Question 23

on a certain high school team, the ratio of sophomores to juniors is 2:3, and the ratio of juniors to seniors is 5:6. Sophomores are what fraction of the whole team?

Answer 23

Soph:Jr = 2:3
Jr : Sr = 5:6
Soph:Jr:Sr = 10:15:18
whole = 10 + 15 + 18 = 43
Soph:whole = 10/43

Question 24

In a certain company, the ratio of programmers to marketers is 3:8; and ratio of customer service reps (CSRs) to marketers is 2:3. If there are 27 programmers, there are how many CSRs?

Answer 24

P/M = 3/8 = 27/M 
1/8 = 9M
M =  72

C/M = 2/3 = C/72
2/1 = C/24
C = 48

Question 25

One cup of butter is enough for 12 or roger’s cookies, and one cup of sugar is enough for 8 of these cookies. If he used five more cups of sugar than of butter, how many cookies did he make?

Answer 25

Combine the ratios :
B:C = 1:12 so B:C = 2/24
S:C = 1:8 and S:C = 3/24
B:S:C = 2:3:24

Use algebra :
5 = cups of sugar - cups of butter
5 = 3n - 2n = n
nb of cookies = 24n = 24 x 5 = 12 x 10 = 120

Question 26

A block of ice in a warm room is melting at a rate of 8 grams/hour. If at noon there are 30 grams of ice, when will the bock first be entirely melted?

Answer 26

simplify
8grams/hour = 30grams/H
4/hour = 15/H

cross multiply
4*H = 15hours

solve
H = 15/4 hrs = 3 + 3/4 hrs

completely melted at 3:45pm

Question 27

A bumblebee’s wing flaps 1440 times in 8 seconds. How many times does it flap in a minute?

Answer 27

1440/8 = 720/4 = 360/2 = 180/1
180 flaps/second
1mn = 60 seconds
180*60 = 10,800

Question 28

if gold has a density of 20grams/cm^3, and the price of gold is $50/gram, then what is the price of the gold in a 2cm x 2cm x 2cm cube of gold?

Answer 28

8cm^3 x 20gram/cm^3 x $50/gram = $8000

by cancelling the units