Need help with 4th grade singapore math (algebra)

[jeffandrobyn2]

100 students took a quiz. The average score was 76pts. the boys average was 80pts. The girls average was 70pts. how many girls participated how do I figure this out the singapore math way? By the way, I am the mom, who doesn't know how to help my daughter. I can figure this out, but in a way that is too advanced for her, I need someone familiar with the Singapore Math system.


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[tkhunny]

Sometimes, you can just guess. You have four pieces of information to help you.

Boys Score - 80
Girls Score - 70
Combined Score - 76
Total Kids - 100

If it was 50 boys / 50 girls, we would get 75 for the combined score. We'll need more boys.

Let's try 60 boys / 40 girls. What is that? Keep adjusting until you find it.

 

[soroban]

Hello, jeffandrobyn2!

Fourth grade? . . . Is Algebra being taught that early?
Without Algebra, tkhunny's suggestion (guessing) is the only way.
Even with Algebra, it is tricky to set up.

The Singapore Math System has some secret weapons in its arsenal?

100 students took a quiz; the average score was 76 pts.
The boys' average was 80 pts. .The girls' average was 70 pts.
How many girls participated?

Recall the formula: .\(\displaystyle \dfrac{\text{Total of scores}}{\text{No. of scores}} \:=\:\text{Average} \quad\Rightarrow\quad \dfrac{T}{N} \:=\: A\)


"100 students had an average of 76."

We have: .\(\displaystyle N = 100,\;A = 76\)

Hence: .\(\displaystyle \dfrac{T}{100} \:=\:76 \quad\Rightarrow\quad T \:=\:7600\)

The total of all the score was 7600 points.


Let \(\displaystyle G\) = number of girls.
Then \(\displaystyle 100-G\) = number of boys.
Let \(\displaystyle T_G\) = total of the girls' points.


"The girls' average was 70."

Then: .\(\displaystyle \dfrac{T_G}{G} \:=\:70 \quad\Rightarrow\quad T_G \:=\:70G\)

The total of the girls' points was \(\displaystyle 70G.\)


The total of the boys' points was \(\displaystyle T_B \:=\:7600 - 70G.\)
. . and there were \(\displaystyle 100-G\) boys.

"The boys' average was 80."

. . \(\displaystyle \dfrac{T_B}{B} \:=\:\dfrac{7600-70G}{100-G} \:=\:80\)


Solve for \(\displaystyle G\!:\;\;7600 - 70G \:=\:80(100-G) \quad\Rightarrow\quad 7600 - 70G \:=\:8000 - 80G\)

. . . . . . . . . . \(\displaystyle 10G \:=\:400 \quad\Rightarrow\quad G \:=\:40\)


40 girls participated.


Even if I knew Algebra in 4th grade,
. . I doubt that I could come up with this solution.

 

[spiritmath]

Average and Ratio

I agree with the start of this problem. We know since the average is 76, that the total score for the 100 students is 7600.

Knowing that the boys average is 80, and the girls average is 70, we see that the boys are 4 away from the group average, and the girls are 6 away from the group average. The this means that there are more boys than girls. In fact, it is inversely proportional. The ratio of boys to girls is 6:4, or 60 boys to 40 girls.

Perhaps a little less confusing than the algebraic approach?

Check:
80 x 60 + 40 x 70 = 7600

 

[jeffandrobyn2]

Update

Thanks all, yes, this is 4th grade! It is a new system adopted from Singapore, they were once the bottom of the barrel for math in the world and now consistently rank 1st or 2nd. They actually start algebra in 2nd grade. The method they use is easy for kids to understand (boy I wish I learned that way!) However, for kids in upper elementary it is a bit more difficult since they have been learning the "old way." They were no less than a year behind when they started these new books. They are young and catching on though! I haven't grasped it completely but I can see how amazing this will be for kids.

That being said, we took the problem to school and the teacher said she had quickly copied some "extra review" pages from the book for the kids to work through before the test. That particular type of problem she said they had not yet covered and she didn't realize or even understand why it was with that chapter.

I like you all was trying to solve it with a massive algebraic equation, but knew that could not be what they were expecting the 4th graders to do. She has not needed to bring her book home for me to look ahead for curiosity sake.