POTW #16 - Get Back into the Habit!

Some measurement practice this week. Don't forget the POTW is a weekly assignment, unless otherwise noted. Further, the RATL needs to be done each Friday as well!

Student made POTWs are still much appreciated. And try to do both POTWs when there are 2 (like this week!)
POTW #16 Grade 7 Question:
 

POTW #16 Grade 8 Question:

 
POTW#15 Solution:

Before we figure out and calculate the answer, we must first convert all the units. In this situation, we will convert to kg.

1 t = 1000 kg. We must multiply 0.09 by 1000 to get kg. 1000 x 0.09 = 90 kg.

1 g = 0.001 kg. This time, we have to divide the grams by 1000 because 1/1000 is 0.001. 81000/1000 = 81 kg

1 mg = 0.000001 kg. It takes 1000000 mg to get to 1 kg. The mg should be divided by 1000000.

45000000/1000000 = 45 kg

Now let’s reword the question to get up to date:

Joey 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.

No siblings have identical weight.

The clue “Lance weighs 45 kg” is the key to finding out each child’s weight. Let’s place that in for the final answer.

Lance = 45 kg

We use this clue and go to the only other clue that has Lance involved. “Sarah and Lance together weigh 84 kg”. Lance takes up 45 kg of the 84 kg. Since Sarah is the only other person, she must take up the rest of the weight. 84 - 45 = 39 kg. Sarah weighs 39 kg.

Lance = 45 kg

Sarah = 39 kg

Lance doesn’t have any more clues. Sarah has an additional clue. “Joey and Sarah together weigh 81 kg”. We know Sarah takes up 39 kg of the 81 kg. Using the same method as before, we can conclude Joey takes the rest of that weight. 81 - 39 = 42 kg. Joey weighs 42 kg.

Lance = 45 kg

Sarah = 39 kg

Joey = 42 kg

The next clue Joey is involved in is “Joey and Bob together weigh 92 kg”. Once again, Joey takes 42 kg of that weight so the rest is Bob’s weight. 92 - 42 = 50 kg. Bob weighs 50 kg.

Lance = 45 kg

Sarah = 39 kg

Joey = 42 kg

Bob = 50 kg

The second last clue is that “Tim and Bob together weigh 90 kg”. Bob weighs 50 kg so Tim weighs the rest. 90 - 50 = 40 kg. Tim weighs 40 kg.

Each of the 5 siblings weigh as shown:

Lance = 45 kg

Sarah = 39 kg

Joey = 42 kg

Bob = 50 kg

Tim = 40 kg

We can now use these weights to answer the next question: The total weight of the siblings.

To identify the total weight, we must add every child’s weight.

45 + 39 = 84. 84 + 42 = 126. 126 + 50 = 176. 176 + 40 = 216.

Each of the 5 siblings together weigh 216 kg.

The question asks how much their family weighs (excluding mom). We need the dad’s weight for that. The dad weighs ¾ of the children’s total weight. This is equivalent to 0.75. However, instead of calculating then adding the children’s weight, we can do it in one. The children are equal to 1/1 or 1. 1 + 0.75 = 1.75. We have to multiply the children’s weight by 1.75 to get the final family weight. 216 x 1.75 = 375 kg.

The entire family weighs 375 kg. If you want to know the dad’s weight, we can multiply 216 by 0.75 or subtract 216 from 375. Both will lead to the result of 162 kg.

To do many units, you need to convert from kg. Here are few you could’ve done.

Mg: Divide by 1000000

Cg: Divide by 100000

g: Divide by 1000

t: Multiply by 1000

Here is a rating system to see how well you performed on the bonus (if you got everything right):

1-3 unit: You’re Good

4 units: Wow!

5-8 units: Unbelievable

9 units: Is that even a thing?

10+ units: Mathematician.

My name is Seayrohn btw (I like clue questions and math).