Problem Solving
Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Solution:
Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by $ 145.
What is the median for: 3 6 40 5 2 793 294 63
Median: 23
Show all outcomes if you toss 2 coins
HH
HT
TH
TT
What is the area for a square with the dimensions 4cm by 4cm?
16cm2
6. Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was:
(a) three times as much, (b) twice as much, (c) the same, (d) half as much, (e) a third as much
Solution:
Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr.
We know that
Speed = Distance/Time.
Or, Time = Distance/Speed.
So, times taken to covered a distance of 50 miles on his first trip = 50/x hr.
And times taken to covered a distance of 300 miles on his later trip = 300/3x hr.
= 100/x hr.
So we can clearly see that his new time compared with the old time was: twice as much.
Answer: (b)
Find Mode(s) for: 5 5 5 5 7 3 4 6 7 7 7 1 2 5 4 2 4 7 4 294 2 4 6 3 6 3 6 7 5 6 5 7 7 75 3 1 2 2 5 6 7 8 5 4 2 4 5 7 8 9 0 0 0 0 0 0 7 5 7 9 6 9 5 6 4 6 3 1 4 6 7 8 9 5 8 4 7 4 6 3 2 1 4 7 8 9 7 8 8 8 8 6 8 6 4 3 2 4 4 4 4 5 76 32
Mode: 4
Show all outcomes if you toss a coin and roll a dice
H1 T1
H2 T2
H3 T3
H4 T4
H5 T5
H6 T6
What is the perimeter for a rectangle with the dimensions 16m by 3m?
38m
Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he:
(a) broke even, (b) lost 4 cents, (c) gained 4 cents, (d) lost 9 cents, (e) gained 9 cents, (f) others
Selling price of the first pipe = $1.20
Profit = 20%
Let’s try to find the cost price of the first pipe
CP = Selling price - Profit
CP = 1.20 - 20% of CP
CP = 1.20 - 0.20CP
CP + 0.20CP = 1.20
1.20CP = 1.20
CP = 1.201.201.201.20
CP = $ 1
Selling price of the Second pipe = $1.20
Loss = 20%
Let’s try to find the cost price of the second pipe
CP = Selling price + Loss
CP = 1.20 + 20% of CP
CP = 1.20 + 0.20CP
CP - 0.20CP = 1.20
0.80CP = 1.20
CP = 1.20/0.80
CP = $1.50
Therefore, total cost price of the two pipes = $1.00 + $1.50 = $2.50
And total selling price of the two pipes = $1.20 + $1.20 = $2.40
Loss = $2.50 – $2.40 = $0.10
Therefore, Mr. Jones loss 10 cents.
Answer: (f) others
Find mean for: 58 84 97 30 40 78 10 15 34 44 39 32 42 85 53 91 97 93 43 66 60 25 16 6 44 39 28 40 85 41 71 67 66 67 14 23 81 97 30 16 5 21 56 45 53 9 67 25 48 78 79 2 26 35 44 20 33 60 39 50 60 85 20 92 94 60 61 86 99 20 6 14 64 93 83 80 6 25 66 21
Mean: 49.7125
What is the probability that Matthew will get a blue or green marble in a bag of 5 yellow, 3 green, 8 turquoise, 10 orange, 23 red and 1287 purple. [ show percent, decimal and fraction ] ( round to nearest thousandths )
3/1336 = 0.002 = 0.2%
What is the circumference of a circle with the radius being 7mm? (pi is 3.14)
43.96mm
Two large and 1 small pumps can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming pool in 4 hours. How many hours will it take 4 large and 4 small pumps to fill the swimming pool.(We assume that all large pumps are similar and all small pumps are also similar.)
Let R and r the rate of work of the large and the small pumps respectively
4(2R + r) = 1 : 2 large and 1 small work for 4 hours to do 1 job
4(R + 3r) = 1 : 1 large and 3 small work for 4 hours to do 1 job
T(4R + 4r) = 1 : Find time T if 4 large and 4 small are to do one job.
Solve for R and r the system of first two equations then substitute in the third and solve for T to find the time. T = 5/3 hours = 1 hour 40 minutes.
Find Mean and Median for: 26 93 74 81 84 69 88 69 100 51 46 36 14 82 24 72 66 55 87 84 42 98 47 47 17 7 71 17 53 1 11 94 69 4 26 96 26 82 26 3
Mean: 53.45 Median: 54
What are the odds in favour of Matthew getting a better mark then Denis if Matthew's mark is from 90% - 100% and Denis gets 92%? ( Every mark is equal chance ) { Round to the nearest thousandths }
8:3 because If Matthew gets 90, 91 and 92, then Matthew doesn't get better.
What is the area of a shape with the diameter being 12km? (pi is 3.14159265 and no rounding)
18.8495559km2
5. A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:
(a) 6 % , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 %
Solution:
Income from $ 4000 at 5 % in one year = $ 4000 of 5 %.
= $ 4000 × 5/100.
= $ 4000 × 0.05.
= $ 200.
Income from $ 3500 at 4 % in one year = $ 3500 of 4 %.
= $ 3500 × 4/100.
= $ 3500 × 0.04.
= $ 140.
Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340.
Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340.
= $ 160.
Total invested amount = $ 4000 + $ 3500 = $7500.
Remaining invest amount = $ 10000 - $ 7500 = $ 2500.
We know that, Interest = Principal × Rate × Time
Interest = $ 160,
Principal = $ 2500,
Rate = r [we need to find the value of r],
Time = 1 year.
160 = 2500 × r × 1.
160 = 2500r
160/2500 = 2500r/2500 [divide both sides by 2500]
0.064 = r
r = 0.064
Change it to a percent by moving the decimal to the right two places r = 6.4 %
Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year.
Answer: (e)
Find Mean, Median and Mode for: 76 77 47 47 15 87 86 18 5 42 51 16 77 20 35 65 98 84 68 62 32 83 7 60 67 82 5 93 31 92 84 34 69 12 94 50 12 46 27 17 77 35 75 78 41 67 84 27 66 73 84 99 5 71 17 61 36 14 42 22 27 13 69 74 47 20 2 22 1 92 28 85 94 18 91 40 45 58 81 42 96 16 12 59 13 38 21 79 11 52 55 42 19 20 59 31 36 44 68 80
Mean: 49.47 Median: 47 Mode: 42 and/or 84
What is the experimental probability of Dima passing in Math class if he has a 60%, 15%, 30% and 67% and the gets another test with a equal chance to get any possible grade? ( 1% - 100% ) [ also this is a joke, the experimental part ] { use the most simplified fraction }
The lowest mark would be a 76% which mean will be 49.6, which is a pass due to rounding up. There is a 25/100 chance for him to pass which is 1/4 (76, 77, 78, 79, 80, ..., 100
What is an area and perimeter of a shape with a semi circle on top and a square under with the dimensions of 7cm by 7cm? (pi is 3.14159265358979 and round to the nearest 10 billionths)
P = 31.9955742876 A = 19.2422550032