Percents and ratios Flashcards
1/3
0.33333
2/3
0.66666
1/5
0.2
2/5
0.4
3/5
0.6
4/5
0.8
1/6
0.166666
5/6
0.833333
1/7
- 14285714
0. 143
1/8
0.125
3/8
0.375
5/8
0.625
7/8
0.875
1/9
0.111111
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?
30% increase = 1.3 (multiplier)
30% decrease = 0.7 (multiplier)
product of multipliers :
100 x 1.3 x 0.7 = $91
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?
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
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
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%
Sheila invests $4000 in an account that yields 6% compounding annually for 8 years. What is the total amount after 8 years?
4000 x (1.06)^8
Susan invests $1000 in an account that yields 5% annual, compounding quarterly, then how much does she have after 6 years?
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
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?
boys = 3n girls = 7n 7n - 3n = 4n = 32 n = 8 boys = 3n = 3 x 8 = 24
boys to girls is 3:5. boys are what fraction of the whole?
3/8
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)
sand : concrete = 2:6 = 1:3
1/3 = 150/x
x = 3*150 = 450kgs of sand
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?
Soph:Jr = 2:3 Jr : Sr = 5:6 Soph:Jr:Sr = 10:15:18 whole = 10 + 15 + 18 = 43 Soph:whole = 10/43
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?
P/M = 3/8 = 27/M 1/8 = 9M M = 72
C/M = 2/3 = C/72 2/1 = C/24 C = 48
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?
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
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?
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
A bumblebee’s wing flaps 1440 times in 8 seconds. How many times does it flap in a minute?
1440/8 = 720/4 = 360/2 = 180/1
180 flaps/second
1mn = 60 seconds
180*60 = 10,800
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?
8cm^3 x 20gram/cm^3 x $50/gram = $8000
by cancelling the units
