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June 22nd, 2018, 05:41 PM   #1
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Averages

I have a few questions on averages. I am curious to see different strategies on how to answer these. How would you answer these using elementary school math ONLY?


1. Jill and Jim are twins. At the age of 2, their average weight is 12 kilograms.
In the next year, Jill gains 2 kilograms and Jim gains 4 kilograms. What is
their average weight when they are 3 years old?

2. The average weight of Mark and Mina is 25 kilograms. A year later, their
average weight is 30 kilograms. During this year, Mina gained 2 kilograms.
How many kilograms did Mark gain?

3. John takes two exams, and his average score is 84. He then gets a score of
100 on the third exam. What is his new average score?

4. After taking two exams, Jane’s average score is 88. What score must Jane
make on the third exam so that her new average score is 90?

5. Sam receives the following scores on his English tests: 63, 84, 96 . What
average score does he need on the last two tests in order to maintain an 85
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June 22nd, 2018, 06:14 PM   #2
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Quote:
Originally Posted by mjsilverfly View Post
1. Jill and Jim are twins. At the age of 2, their average weight is 12 kilograms.
In the next year, Jill gains 2 kilograms and Jim gains 4 kilograms. What is
their average weight when they are 3 years old?
(a + b) / 2 = 12
(a + b + 6) / 2 = ?

OR: they gained an average of (2 + 4)/2, so new average = ?
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June 22nd, 2018, 06:27 PM   #3
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Thank you. I guess I am most interested in how to go about numbers 4 and 5 without using algebra. How would you teach this without using algebra? The only way I can think is to do number 5 is: (243 + x) / 5 = 85, then solve for x.
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June 22nd, 2018, 06:40 PM   #4
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Quote:
Originally Posted by mjsilverfly View Post
The only way I can think is to do number 5 is:
(243 + x) / 5 = 85, then solve for x.
That should be (243 + 2x) / 5 = 85

WHY without using algebra?
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June 22nd, 2018, 08:10 PM   #5
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Right, I was thinking of x as the sum of the 2 scores, then I was going to divide x by 2 to get the average score. But, yes, thank you for that. I am supposed to teach how to do this to students who don't yet know algebra.
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June 23rd, 2018, 02:35 AM   #6
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[QUOTE=mjsilverfly;595808]I have a few questions on averages. I am curious to see different strategies on how to answer these. How would you answer these using elementary school math ONLY?[/math]
The "average" of n numbers is their total divided by n. Conversely, the total is the average multiplied by n.


Quote:
1. Jill and Jim are twins. At the age of 2, their average weight is 12 kilograms.
In the next year, Jill gains 2 kilograms and Jim gains 4 kilograms. What is
their average weight when they are 3 years old?
During that year the twins gained a total or 2+ 4= 6 kg so they gained an average of 6/2= 3 kg. Their average weight will now be 12+ 3= 15 kg.

Quote:
2. The average weight of Mark and Mina is 25 kilograms. A year later, their
average weight is 30 kilograms. During this year, Mina gained 2 kilograms.
How many kilograms did Mark gain?
There average weight changed by 30- 25= 5 kg, a total of 2*5= 10 kg. Since Mina gained 2 kg, Mark gained 10- 2= 8 kg.

Quote:
3. John takes two exams, and his average score is 84. He then gets a score of 100 on the third exam. What is his new average score?
The average score on two exams was 84 so the total score was 2(84)= 168. After the third exam the total was 168+ 100= 268. His average now is 268/3= 89 and 1/3.

Quote:
4. After taking two exams, Jane’s average score is 88. What score must Jane make on the third exam so that her new average score is 90?
The total score on the first two exams is 2(88 )= 176. After the third exam the total must be 3(90)= 270. She must make 270- 176= 94 on the third exam.

Quote:
5. Sam receives the following scores on his English tests: 63, 84, 96 . What average score does he need on the last two tests in order to maintain an 85
His total score on those three tests was 63+ 84+ 96= 243. In order to get an average of 90 on 5 tests, he must get a total of 5(90)= 450. So on the last two tests he must get a total of 450- 243= 207. That is an average of 207/2= 103.5 on the last two tests.
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