Word problem for 6th grader (exemplar)

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Word problem for 6th grader (exemplar)

Postby LilyBug05 » Mon Sep 19, 2016 4:35 pm


Students surveyed boys and girls separately to determine which sport was enjoyed the most. After completing the boy survey, it was determined that for every 3 boys who enjoyed soccer, 5 boys enjoyed basketball. The girl survey had a ratio of the number of girls who enjoyed soccer to the number of girls who enjoyed basketball of 7:1. If the same number of boys and girls were surveyed, and 90 boys enjoy soccer, how many girls enjoy each sport?

Please help! Mom is bad at math. Can you show the work so she knows how to get the answer? Thank you!
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Re: Word problem for 6th grader (exemplar)

Postby Guest » Mon Sep 19, 2016 6:26 pm

for every 3 boys who enjoyed soccer, 5 boys enjoyed basketball:
So 3 out of 8 enjoyed soccer (8 comes from 3+5)
Or another way of saying this is 3/8 of the total number of boys enjoyed soccer.

90 boys enjoy soccer:
We know that 3/8 of the total number of boys enjoyed soccer, and that 90 boys enjoyed soccer.
So 3/8 of the total number of boys = 90 boys.
Divide both sides by 3
So 1/8 of the total number of boys = 30 boys
Multiply both sides by 8
So the total number of boys = 240.

the same number of boys and girls were surveyed:
We know that the total number of boys = 240, and that total number of boys = total number of girls.
So total number of girls is 240.

ratio of the number of girls who enjoyed soccer to the number of girls who enjoyed basketball of 7:1
This means that for every 7 girls that like soccer, there is 1 girl that likes basketball.
(Just like before it is easier to work with fractions than ratios, so we should convert the ratio to fractions.)
So 7 out of 8 liked soccer (8 comes from 7+1)
Or 7/8 of the total number of girls liked soccer, remember that there are 240 girls in total.
So 7/8 of 240 girls like soccer ("of" means multiply when considering fraction word problems)
So [tex]\frac{7}{8}\times 240 = 210[/tex] girls like soccer. That leaves 30 girls who like basketball (30=240-210).

Doing it the long way, we could also have worked out the basketball loving girls by saying:
1 out of 8 like basketball (8 comes from 7+1)
Or 1/8 of the total number of girls liked basketball, remember that there are 240 girls in total.
So 1/8 of 240 girls like basketball ("of" means multiply when considering fraction word problems)
So [tex]\frac{1}{8}\times 240 = 30[/tex] girls like basketball.

General rules:
It is easier to work with fractions than ratios.
Convert ratios to fractions by taking one of the numbers over the sum of numbers.
For example 2:3 becomes 2/5 and 3/5 (the 5 comes from 2+3).
4:2 becomes 4/6 and 2/6 (the 6 comes from 4+2)
5:2:7 becomes 5/14, 2/14, and 7/14 (the 14 comes from 5+2+7)
If you see the expression "some fraction" of "something" this translates to "some fraction"[tex]\times[/tex]total number of "something".
For example 1/4 of adults becomes [tex]\frac{1}{4}\times[/tex] total number of adults.
2/7 of pages in a book means [tex]\frac{2}{7}\times[/tex] total number of pages in a book.
If you see the expression "something" is "some other thing" this translates to "something"="some other thing".
(Also the word "same" also translates into =)
For example the number of dogs is 30 becomes number of dogs=30.
When you have an equal sign you can do the same thing to both sides of the equal sign to simplify things
For example[tex]\frac{1}{3}\times[/tex] number of teachers = 2
Multiply both sides by 3 to get number of teachers = 6
or for example number of apples -10 = 4
Add 10 to both sides to get number of apples = 14

Hope this helped,

R. Baber.
Guest
 

Re: Word problem for 6th grader (exemplar)

Postby Guest » Mon Sep 19, 2016 8:15 pm

Unfortunately I'm not familiar with the 6th Grade curriculum, but having had a quick look online, it seems you are meant to do these questions by considering how the numbers scale.

for every 3 boys who enjoyed soccer, 5 boys enjoyed basketball:
So in a typical group of 8 boys, 3 liked soccer, 5 liked basketball. (The 8 came from 3+5.)
Now consider if we had 2 group of 8 boys, that's 16 boys in total, 6 would like soccer, 10 would like basketball (all the numbers have been multiplied by 2)
If we had 3 groups of 8 boys, that's 24 boys in total, 9 would like soccer, 15 basketball (the numbers have been multiplied by 3)
Continuing the pattern we can create a table:
1 group, 3 like soccer, 5 like basketball, 8 in total
2 group, 6 like soccer, 10 like basketball, 16 in total
3 group, 9 like soccer, 15 like basketball, 24 in total
4 group, 12 like soccer, 20 like basketball, 32 in total
5 group, 15 like soccer, 25 like basketball, 40 in total
...

90 boys enjoy soccer:
If the second column is 90, how many groups will we have?
The second column is 3 times the first column. So "something" times 3 equals 90. That "something" is 90/3=30.
So we have 30 groups
3[tex]\times[/tex] 30 = 90 like soccer
5[tex]\times[/tex] 30 = 150 like basketball
8[tex]\times[/tex] 30 = 240 boys in total.

the same number of boys and girls were surveyed:
Number of girls = 240

ratio of the number of girls who enjoyed soccer to the number of girls who enjoyed basketball of 7:1
Like before we can create a table, where we consider groups of 8 girls (because 8=7+1).
1 group, 7 like soccer, 1 like basketball, 8 in total
2 group, 14 like soccer, 2 like basketball, 16 in total
3 group, 21 like soccer, 3 like basketball, 24 in total
4 group, 28 like soccer, 4 like basketball, 32 in total
5 group, 35 like soccer, 5 like basketball, 40 in total
...

How many groups do we have if there are 240 girls in total.
The last column is always 8 times the first. So something times 8 =240. That something is 240/8 = 30.
So we have 30 groups
7[tex]\times[/tex] 30 = 210 girls like soccer
1[tex]\times[/tex] 30 = 30 girls like basketball
8[tex]\times[/tex] 30 = 240 girls in total.

Hope this helped,

R. Baber.
Guest
 


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