by **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.