Fiona has mentioned she has some question ideas. I am always open to ideas for questions/solutions if you have them. Please see me if you'd like. (Mr. Milette)
POTW #11 Solution:
POTW #12 Gr 7 Question:
POTW #12 Gr. 8 Question:
Sunday, November 25, 2018
POTW #12 - Up for Question Ideas!
Remember if there are TWO POTW questions for the week, please try to do both.
Fiona has mentioned she has some question ideas. I am always open to ideas for questions/solutions if you have them. Please see me if you'd like. (Mr. Milette)
POTW #11 Solution:
POTW #12 Gr 7 Question:
POTW #12 Gr. 8 Question:
Fiona has mentioned she has some question ideas. I am always open to ideas for questions/solutions if you have them. Please see me if you'd like. (Mr. Milette)
POTW #11 Solution:
POTW #12 Gr 7 Question:
POTW #12 Gr. 8 Question:
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Grade 7 POTW
ReplyDeleteFor this question, we simply just have to find out how much time 7/8 from 4-5 is in the hours/minutes/seconds. Okay, so from 4-5, 1 hour has passed or 60 minutes and the minute hand moved 360 degrees or a full circle. We just have to find out how much 7/8 of 60 is. This is pretty simple as we just have to multiply 60 by 7/8 or divide it by 8 and multiply by 7.
60/8 = 7.5
7.5 x 7 = 52.5 minutes = 52 minutes and 1/2 minute = 52 minutes and 30 seconds
4 hours 52 minutes 30 seconds
Therefore, the time would be 30 seconds past 4:52.
Grade 8 POTW
ReplyDeleteFirst, I'll list the important information.
- 3L = 7%
- 4L = 20%
- Bulk = 5%
- 3L + 4L + BulkL = 8%
I'm just going to go straight into it (done before).
B = Bulk Supply Liters
T = Total Liters
3/100 = 0.03
0.03 x 7 = 0.21L = 210 mL
4/100 = 0.04
0.04 x 20 = 0.8L = 800 mL
3 + 4 = 7L = 7000 mL
0.21 + 0.8 = 1.01L = 1010 mL
To review what we have, 7L = 1.01L of glycerine.
3 + 4 + B = 7 + B = T
0.21 + 0.8 + 0.05B = 1.01 + 0.05B = 0.08T
Through substitution:
0.08T = 0.08(3 + 4 + B) = 0.08(7 + B) = 0.56 + 0.08B
Now we can solve:
1.01 + 0.05B = 0.56 + 0.08B
1.01 + 0.05B - 0.56 = 0.08B
0.45 + 0.05B - 0.05B = 0.08B - 0.05B
0.45 = 0.03B
45 = 3B
15 = B
Therefore, 15L of antifreeze must be added to create a 0.08L glycerine mixture.
I accidentally wrote 0.08L glycerine. *8% or 0.08.
Deleteif it is between 4 and 5 it has to be 4:__:__
ReplyDeletenow we know that in a hour there is 60 minutes so 60* 7/8= the exact amount of minutes and seconds.
60*7/8=420/8
402/8=50.25 minutes
25=1/4
1 fourth of 60 seconds= 15 seconds
4:50:15 is the exact time
Grade 7 POTW
ReplyDeleteThe question is very straightforward. The clock only has an hour hand and it is in between 4 and 5. The hour hand of the clock is as states in the question, 7/8 past 4 and 1/8 below 5. The time in minutes from 4 to 5 is 60 as 1 hour is 60 minutes. This means we have to multiply 60 by 7/8. This means we have to divide 60 by 8 and then multiply it by 7 because 60 divided by 8=1/8 x 7=7/8. 60/8=7.5 x 7=52.5. 7/8 of 60 is 52.5 which is technically 52 minutes and 30 seconds.
52 minutes and 30 seconds past 4 makes the time 4:52:30 or 30 seconds past 4:52.
8/8= 5:00
ReplyDelete60 minutes in 1 hour
60/8=7.5
each 1/8 is 7.5 minutes
7.5*7=52.5
0.5 of 1 minute is 30 seconds
4:00+52minutes+30seconds=
4:52:30
Hour/Minute/Second
POTW:
ReplyDeleteWe know that one hour has 60 minutes. The hour hand is 7/8 of the distance between '4' and '5'. So we multiply 60 by 7/8 to find the time. 60*7/8 = 52.5
So, it 4:52.
But we need to find the seconds as well. 0.5 means 1/2. Half of 60 is 30. So the time is:
4:52:30 (HOUR/MINUTE/SECOND)
I will make this an expression to make it easier:
ReplyDeletex : x : x
Now, since the hour hand is between 4 and 5 the hour is 4:00(Advanced expression below)
4 : x : x
Since there are 60 minutes in an hour and the hour hand is 7/8 the way to 5 we will multiply 60 by 7/8
60 x 7/8 = 52.5
Now that we found the minutes the new expression is now 4 : 52 : x
The last part of the solution is that the 0.5 left of 52.5 is equal to half. Now divide 60 by 2. The answer is 30 so the full expression is...…..
4 : 52 : 30
Starting off, we know that one hour has 60 minutes in it. To find out what ⅞ of 60 minutes is, we multiply 60 by ⅞. 60*⅞= 52.5. This number is how much of an hour ⅞ is. We add that onto four o’clock to get 4:52.5. However, you can’t have .5 as your seconds, instead we change it into half a minute, 30 seconds.
ReplyDeleteThis leaves us with:
It is: 4:52:30 (hour:minute:second)
Grade 7 POTW:
ReplyDeleteInfo:
- 7/8 between 4 and 5.
Find:
- Exact time
I do remember doing a unit on clocks and angle during spirit of math, and I know that each minute, the minute hand move 6 degrees and the hour hand moves 0.5 degrees (because in an hour it moves 1/12 of the clock which is 30 degrees, and each hour has 60 minutes so you divide and you get 0.5 of a degree). The minute hand moves 360 degrees per 60 minutes, so we have to find 7/8 of 60 now.
60 x 7/8 = 52.5
This is equal to 52 and 30 seconds (because time is weird and half is 30 instead of 50 and thats confusing, but that’s life and life is confusing).
(Therefore) the time is 4:52:30
Grade 8 POTW:
ReplyDelete- 3L of anti-freeze which is 7% glycerine
- 4L of anti-freeze which is 20% glycerine
- Bulk of 5% glycerine
- Added 3L and 4L then added bulk.
How much antifreeze is needed of anti-freeze to make 8% glycerine?
From what I am understanding, I need to figure out the percentage of glycerine from the two bottles (3L and 4L) and find out how much more I need to add to make the mixture 8% glycerine.
To find the amount of glycerine in the first mixture (I’m going to name the mixture of the 3L and 4L bottle x for easier…. referral :)
Anyways, to find the amount of glycerine in the mixture, we need to figure out the amount of glycerine per bottle by multiplying the percentage with its respective bottle measure.
3 x 0.07= 0.21 L or 210 mL
4 x 0.2 = 0.8 L or 800 mL
This would total 210 + 800 = 1010 mL or 1.01L of glycerine.
The ratio of antifreeze to glycerine is 7L : 1.01 L.
Using this, we can make uno expressioneeeeee:
Using the variable y for the litres of bulk supply needed, we can make this equation.
0.08(7 + y)
0.56 + 0.08 y.
1.01+0.05y = 0.56 +0.08y
0.05y - 0.08y=0.56 - 1.01
-0.03y=-0.45
y=15
Therefore, the required amount is 15 L of antifreeze
To get to the answer for this question, I just need to find out how much 7/8 is of 60 minutes (since 4:00-5:00 is equal to an hour). This is very simple since I would just need to divide 60 by 8, then multiply the quotient by 7 to get to ⅞ of 4:00-5:00.
ReplyDelete60 / 8 = 7.5
7.5 x 7 = 52.5
52.5 = 52 minutes and 30 seconds
The answer would be 4:52:30 or 30 seconds past 4:52.
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ReplyDeleteThe clock only shows the hour hand
ReplyDeleteThe hour hand is 7/8 in the middle of 4 and 5
First, I would have to divide 60 in 8
60/8=7.5
Then, I need to multiply 7.5 by 7, so I can get 7/8 and not 1/8.
7.5x7=52.5
52.5 is 52 mins and 30 secs
Time: 4:52:30
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ReplyDeleteWe know that since the hour hand is in between 4 and 5, the hour is 4. Now, we must find ⅞ of 4 to 5, or how many minutes in ⅞ in 1 whole. To do this, we must find ⅞ with a denominator of 60. To do this, I would have to do 7 / 8 * 60, which equals 52.5. So, I know that the time is 4:52:30. The time is 4 hours, 52 minutes, 30 seconds.
ReplyDelete