Happy new year and welocme back to the POTW! Thanks for this week's
student submission of the POTW. Do you know who's it is?
POTW #15 Grade 7/8 Question:
The 5 Siblings!
The 5 siblings, Joey, Bob, Sarah, Lance, and Tim decide to challenge their dad to a guessing game.
The siblings would have to do no chores for a week if they win. If they lose, they must do their father’s
chores! The children ask their dad to identify each of their weights after giving some clues. If one is
incorrect, their dad loses. What should the dad guess for each weight? What are the 5 children’s total
weight? The dad weighs ¾ of the children’s total weight. How much does the entire family (excluding
mom) weigh?
MEASUREMENT UNIT EXTENSION: Try providing your answers in as many different units as you can.
Clues:
Joey and Bob together weigh 92 kg.
Sarah and Lance together weigh 84 kg.
Tim and Bob together weigh 0.09 t.
Joey and Sarah together weigh 81000 g
Lance weighs 45000000 mg.
No siblings have identical weight.
Grade 7/8
ReplyDeleteJoey = 42 kg
Bob = 50 kg
Sarah = 39 kg
Lance = 45 kg
Tim = 40 kg
Children Total Weight = 216 kg
Dad = 162 kg
Family = 378 kg
Work done on paper.
I think the person who made this question would spend the time to make the question and even have the time. They would love math. They probably also like mystery solving questions. The only few people I know who have these qualities is someone like...
CINDY HUA!!! (I will probably come back to this comment to fix the guess or answers)
Grade 7/8 POTW:
ReplyDeleteInfo:
- Joey: ?
- Bob: ?
- Sarah: ?
- Lance: 45000000 mg
- Tim: ?
- Joey and Bob together weigh 92 kg.
- Sarah and Lance weigh 84 kg.
- Tim and Bob together weigh 0.09 t.
- Joey and Sarah together weigh 81000 g.
- No siblings have identical weights.
Questions:
- What should the dad guess for each weight?
- What are the 5 children's total weight?
- The dad weighs 3/4 of the children's total weight, how much does the family weigh together?
First, I am going to convert all of the clues to kg.
- Lance: 45 kg
- Joey and Bob together weigh 92 kg.
- Sarah and Lance weigh 84 kg.
- Tim and Bob together weigh 90 kg.
- Joey and Sarah together weigh 81 kg.
- No siblings have indentical weights.
If Sarah and Lance weigh 84 kg, and Lance is 45 kg, I can find how much Sarah weighs by subtracting 84- 45= 39 kg.
And if Joey and Sarah weigh 81 kg together, I can find Joey's weight by subtracting 81-39 = 42. And if Joey and Bob weigh 92 kg together, I can find Bob's weight by subtracting 92-42=50. If Tim and Bob weigh 90 kg, I can find Tim's weight by subtracting 90-50 = 40
- Joey: 42 kg (42000 g, 42000000 mg)
- Bob: 50 kg (50000 g, 50000000 mg)
- Sarah: 39 kg (39000 g, 39000000 mg)
- Lance: 45kg (45000 g, 45000000 mg)
- Tim: 40 kg (40000 g, 40000000 mg)
Together, they weigh 216 kg together. If their dad is 3/4 of their weight, I can multiply 216 by 0.75 to find 3/4. Their dad weighs 162 kg. The wholef amily weighs 378 kg.
TADA!!!
Please tell me if I went wrong somewhere.
Grade 7/8 POTW
ReplyDeleteThe dad should guess that Lance weighs 45 kg, Sarah weighs 39kg, Joey weighs 42kg, Bob weighs 50 kg, and Tim weighs approximately 31.6 kg. The total weight of all 5 siblings is approximately 207.6 kg, which means that the dad weighs around 155.7 kg. Finally, the total weight of the entire family (excluding the mom) is around 363.3 kg.
I'm not even in the mood to deal with conversions right now, so let's get this over quickly.
ReplyDeleteFirst of all, I will convert all of the weights to Kg.
Joey and Bob 92 Kg.
Sarah and Lance 84 Kg.
Tim and Bob 90 Kg(0.09 T)
Joey and Sarah 81 Kg(81000 g)
Lance weights 45000000 mg, which is 45 kg.
Now that I have all of the answer in Kg, this means that I can figure out the weights using the given clues.
Lance = 45 Kg(0.045 tons, 45 kg, 450 hectograms, 4 500 decagrams, 45 000 grams,
450 000 decigrams, 4 500 000 milligrams, 4 500 000 000 micrograms)
Sarah = 84 - 45 = 39 Kg(0.039 tons, 39 kg, 390 hectograms, 3 900 decagrams, 39 000 grams, 390 000 decigrams, 3 900 000 milligrams, 3 900 000 000 micrograms)
Joey = 81 - 39 = 42 Kg(0.042 tons, 42 kg, 420 hectograms, 4 200 decagrams, 42 000 grams, 420 000 decigrams, 4 200 000 milligrams, 4 200 000 000 micrograms)
Bob = 92 - 42 = 50 Kg(0.05 tons, 50 kg, 500 hectograms, 5 000 decagrams, 50 000 grams, 500 000 decigrams, 5 000 000 milligrams, 5 000 000 000 micrograms)
Tim = 90 - 50 = 40 Kg(0.04 tons, 40 kg, 400 hectograms, 4 000 decagrams, 40 000 grams, 400 000 decigrams, 4 000 000 milligrams, 4 000 000 000 micrograms)
Since I have all of these weights, I can add them up to get 216.
The father is 3/4 of this weight, so I multiply 216 and 3/4(0.75) to get 162 Kg.
The total weight would be 216 + 162 = 378 Kg.
And there we go! Answer done.
By the way, the best answer would probably to mess around with the weights because once that happens, no chores for the kids. Fun! And also, I kind of decided to use micrograms because it did say it on the worksheet we did XD.
Joey+Bob=92 Kg
ReplyDeleteSarah+Lance=84 Kg
Tim+Bob=90 Kg
Joey+Sarah=81 Kg
Lance=45 kg
Lance is 45kg, so we know Sarah and Lance equals 84 kg. We could just subtract 84 and 45. That'll equal 39kg. So now we know Sarah is 39kg. And if just continue, like Sarah-Joey then Joey-Bob and then Bob-Tim, we can figure out all their weights.
Lance=45kg
Sarah=39kg
Joey=42kg
Bob=50kg
Tim=40kg
Add them together we get 216kg. Since father is 3/4 of their weight, we can just multiply 216 by 0.75 then add them both together. And we get 378kg in total.
84 - 45 = 39 kg 39000 g 39000000 mg(Sarah)
ReplyDelete81 - 39 = 42 kg 42000 g 42000000 mg(Joey)
92 - 42 = 50 kg 50000 g 50000000 mg(Bob)
90 - 50 = 40 kg 40000 g 40000000 mg(Tim)
45 kg 45000 g 45000000 mg(Lance)
39+42+50+40+45 = 216 kg 216000 g 216000000 mg
Father = ¾ of 216 = 162 kg
216 + 162 = 378 kg
I did this by first subtracting Lance’s weight from the combined weight of 84 kg with Sarah. That gave me Sarah’s weight of 39 kg which I can use for the combined weight of Sarah and Joey and so on. After going over all the clues I finally got the answers and added them together for the total weight of the 5 children. The father’s weight is 162 kg which I found out by doing the math of ¾ of 216 kg which is 162 kg. The total is then 378 kg.
Lance = 45k
ReplyDeleteSarah = 84 - 45 = 39kg
Joey = 81 - 39 = 42kg
Bob = 92 - 42 = 50kg
Tim = 90 - 50 = 40kg
total = 216
Dad = 216 x 0.75 = 162
216 + 162 = 378
therefore, their total weight is 378.
I would convert them to all of the possible different units but I'm too lazy.
Everything converted into kg would be..
ReplyDeleteJoey and Bob together weigh 92 kg.
Sarah and Lance together weigh 84 kg.
Tim and Bob together weigh 90 kg.
Joey and Sarah together weigh 81 kg
Lance weighs 45 kg.
Sarah = 39 kg
Joey = 42 kg
Bob = 50 kg
Tim = 40 kg
Adding them all together would equal to 216 kg. 3/4 of 216 is 162. The total weight is 378 kg.
Grade 8 POTW:
ReplyDeleteThe total weight is 378 kg. All my work and conversions are done in my math notebook.
POTW #15
ReplyDeleteClues:
Joey + Bob = 92 kg
Sarah + Lance = 84 kg.
Tim + Bob = 0.09 t.
Joey + Sarah = 81000 g
Lance = 45000000 mg
No siblings have identical weight
Dad = 3/4 of children's weight
Find: Each child's weight. 5 kids' weight total. Weight of entire family (minus mom)
First step: Convert into same units (kg in this case)
Joey + Bob = 92 kg
Sarah + Lance = 84 kg
Tim + Bob = 90 kg
Joey + Sarah = 81 kg
Lance = 45 kg
Second Step: Find each weight
Sarah and Lance = 84, so 84 - 45 = 39
Joey and Sarah = 81, so 81 - 39 = 42
Joey and Bob = 92, so 92 - 42 = 50
Bob and Tim = 90 kg, so 90 - 50 = 40
Sarah = 30 kg
Joey = 42 kg
Bob = 50 kg
Tim = 40 kg
Lance = 45 kg
Therefore, Sarah weighs 39 kg, Joey weighs 42 kg, Bob weighs 50 kg, and Tim weighs 40 kg, and Lance weighs 45 kg.
To find the total weight, just add each number together;
39 + 42 + 50 + 40 +45 = 216 kg
Therefore the total weight of the 4 kids is 216 kg
To find 3/4 of 216 for the dad's weight:
216 / 4 = 54
54 x 3 = 162
Therefore the dad weighs 162 kg
To find the total of the entire family, just add the sum of the kids, plus dad's weight;
216 + 162 = 378
Therefore the total weight of the family (minus mom) is 378 kg.
POTW #15:
ReplyDeleteLance = 45 kg
Sarah = 39 kg
Bob = 50 kg
Joey = 42 kg
Tim = 40 kg
Kids Total: 216 kg
Dad = 162
162 = 216*0/75
Total: 378 kg
Hard copy work
Lance is 45kg
ReplyDeleteSarah is 39kg
Bob is 50kg
Joey is 42kg
Tim is 40kg
The kid's total is 216kg
The dad is 162kg
The total is 378kg
I used the process of elimination to work through all the clues and assign various weights.
Lance is 45 kg
ReplyDeleteSarah is 39 kg
Bob is 50 kg
Joey is 42 kg
Tim is 40 kg
The total of the kids is therefore 216kg
The dad must be 162kg, making the total 378kg.
You have to work backwards and use the process of elimination to get answers.
POTW #5
ReplyDeleteFor this question, you have to really work backwards, and use trial and error to find the weights. Firstly let's look at the clues...
Joey and Bob together weigh 92 kg.
Sarah and Lance together weigh 84 kg.
Tim and Bob together weigh 0.09 t.
Joey and Sarah together weigh 81000 g
Lance weighs 45000000 mg.
No siblings have identical weight
And after A LOT of conversions and trial and error, I managed to get the weights of all five kids.
Bob is 50 kg
Joey is 42 kg
Sarah is 39 kg
Lance is 45 kg
Tim is 40 kg
Added all together, their combined weight would be 216 kg, meaning that their dad's weight has to be 162 kg (3/4 of 216). All I have to do now is add together 216 kg and 162 kg, which equals 378 kg.
That is my answer for this week's POTW!
OH bOY
ReplyDeleteOkay so these were the clues given to us
Joey + Bob = 92 kg
Sarah + Lance = 84 kg.
Tim + Bob = 0.09 t.
Joey + Sarah = 81000 g
Lance = 45000000 mg
No siblings have identical weight
Dad = 3/4 of children's weight
So I need to find Everyone's individual weight, 5 kids' weight together, as well as the weight of entire family except for the mother.
If I learned anything from the FDPR unit I have to convert everything to the same format thing. so
Joey + Bob = 92 kg
Sarah + Lance = 84 kg
Tim + Bob = 90 kg
Joey + Sarah = 81 kg
Lance = 45 kg
We were given Lance's weight, which is 45kg
Sarah and Lance = 84, so 84 - 45 (Lance's weight) = 39kg (Sarah's weight)
Lance = 45kg
Sarah = 39kg
Joey and Sarah = 81, so 81 - 39 (Sarah's weight) = 42 (Joey's weight)
Lance = 45kg
Sarah = 39kg
Joey = 42kg
Joey and Bob = 92, so 92 - 42 (Joey's weight) = 50kg (Bob's weight)
Lance = 45kg
Sarah = 39kg
Joey = 42kg
Bob = 50kg
Bob and Tim = 90 kg, so 90 - 50 (Bob's weight) = 40kg (Tim's weight)
Lance = 45kg
Sarah = 39kg
Joey = 42kg
Bob = 50kg
Tim = 40kg
45 + 39 + 42 + 50 + 40 = 216kg
The total weight of the kids = 216kg
Dad weighs 3/4 of the kid's total weight
216 ÷ 4 = 54
54 x 3 = 162
Dad = 162kg
216kg + 162kg = 378kg (total weight of the family without mom)
POTW #15:
ReplyDeleteInformation when obtained from the question:
Joey and Bob together weigh 92 kg.
Sarah and Lance together weigh 84 kg.
Tim and Bob together weigh 0.09 t.
Joey and Sarah together weigh 81000 g
Lance weighs 45000000 mg.
No siblings have identical weight.
Dad weighs 3/4 of the children's total weight
So we should first convert each weight into the same measurement (KG) so it'll be easier to answer the rest of the question and not get confused.
Joey = ?
Bob = ?
Sarah = ?
Lance = 45000000 mg = 45 kg
Tim = ?
So the question states that Sarah and Lance together, both weigh 84 kg.
84 - 45 (Lance's given weight) = 39 kg
Joey = ?
Bob = ?
Sarah = 39 kg
Lance = 45 kg
Tim = ?
Then, the question also states that Sarah and Joey weigh 81 kg (81000 g) together.
81 - 39 = Joey's weight (42 kg)
Joey = 42 kg
Bob = ?
Sarah = 39 kg
Lance = 45 kg
Tim = ?
Then we have Joey and Bob together weighing 92 kg.
92 - Joey's weight = Bob's weight (50 kg)
Joey = 42 kg
Bob = 50 kg
Sarah = 39 kg
Lance = 45 kg
Tim = ?
Now lastly, Bob and Tim weigh 90 kg (0.09 t) together
90 kg - Bob's weight = Tim's weight (40 kg)
Joey = 42 kg
Bob = 50 kg
Sarah = 39 kg
Lance = 45 kg
Tim = 40 kg
The children's total weight is 216 kg
If the dad weighs 3/4 of the group of children;
216 / 4 = 54
54 x 3 = 162
216 + 162 = 378 kg
The entire family (excluding mom) weighs 378 kg
Joey and Bob together weigh 92 kg.
ReplyDeleteSarah and Lance together weigh 84 kg.
Tim and Bob together weigh 0.09 t.
Joey and Sarah together weigh 81000 g
Lance weighs 45000000 mg.
The first thing is to convert all of the weights to the same unit. I chose kg.
Joey and Bob = 92 kg.
Sarah and Lance = 84 kg.
Tim and Bob = 90 kg.
Joey and Sarah = 81 kg.
Lance = 45 kg.
Since we know Lance's exact weight, we can also figure out Sarah's.
84 - 45 = 39.
We now know that Lance weighs 45 kg and Sarah weighs 39 kg. Using this, we can also figure out Joey's weight.
81 = 39 = 42
We now know that Lance weighs 45 kg, Sarah weighs 39 kg, and Joey weighs 42 kg. Since we know Joey's weight, we can figure out Bob's weight.
92 - 42 = 50.
We now know that Lance weighs 45 kg, Sarah weighs 39 kg, Joey weighs 42 kg, and Bob weighs 50 kg. Lastly, we can easily figure out Tim's weight.
90 - 50 = 40.
We now know that Lance weighs 45 kg, Sarah weighs 39 kg, Joey weighs 42 kg, Bob weighs 50 kg, and Tim weighs 40 kg. After adding all of these together, we end with a total of 216 kg. Since the dad weighs 3/4 of all the children, we can do 216 / 4 to get 54, and then do 216 - 54 to get 162 kg. We then add 162 and 216 together to achieve a grand total of 378 kg.
POTW #15
ReplyDeleteInformation:
Joey and Bob together weigh 92 kg.
Sarah and Lance together weigh 84 kg.
Tim and Bob together weigh 0.09 t.
Joey and Sarah together weigh 81000 g.
Lance weighs 45000000 mg.
No siblings weigh the same.
Dad weighs 3/4 of the children's total weight.
Next, I'm going to convert everything to the same unit of measurement, to make things easier.
Joey = ?
Bob = ?
Sarah = ?
Lance = 45000000 mg = 45 kg
Tim = ?
Since we know Lance's exact weight, we can now figure out what Sarah's exact weight is.
84 - 45 = 39.
Know we know that Lance weighs 45 kg, and that Sarah weighs 39 kg. Now that we know this, we can find out Joey's weight.
81 - 39 = 42.
So far, we know that Lance weighs 45 kg, Sarah weighs 39 kg, and Joey weighs 42 kg. We know Joey's weight, and therefore, now we can figure out Bob's weight.
92 - 42 = 50.
Now, we know that Lance weighs 45 kg, Sarah weighs 39 kg, Joey weighs 42 kg, and Bob weighs 50 kg. The last person is Tim, and we can easily figure out what his weight is.
90 - 50 = 40.
Now, we can fill in the chart that we had in the beginning:
Joey = 42 kg.
Bob = 50 kg.
Sarah = 39 kg.
Lance = 45 kg.
Tim = 40 kg.
Since the dad weighs 3/4 of all the children, we must find the grand total of all the children's weight (216) divided by 4, to get 54. We then do 216 - 54, to get 162 kg. So, we then add 162 and 216 together, to achieve a grand total of...
*drumrolll pleeeaseee*
378 kg!!
Joey weighs 42 kg
ReplyDeleteBob weighs 50 kg
Sarah weighs 39 kg
Lance weighs 45 kg
Tim weighs 40 kg
Dad weighs 162 kg
The family (without mom) altogether weighs 378 kg
Bob - 50 kg
ReplyDeleteTim - 40 kg
Lance - 45 kg
Joey - 42 kg
Sarah - 39 kg
Dad - 162 kg
Family - 378 kg
Work done on paper.