The ratio of 6th graders to 7th graders in a mathcounts club is 5: 4. the ratio of 8th graders to 7th graders in the same club is 3: 2. if there are 18 8th graders in the club, how many 6th graders are in the club?

To solve this problem, KROW SDAWKCAB. (That's WORK BACKWARDS spelled backwards.)

We are told that there's a 3:2 ratio of 8th graders to 7th graders in the club. Let x be the number of 7th graders in the class. We set a proportion. The proportion puts the ratio on one side, how many students on the other. Tops are the 8th graders, bottoms are the 7th graders.

You can solve it by cross multipling or by noticing what happens between the fractions. On the top how did you go from 3 to 18? You multiplied by 6. So the same thing must happen on the bottoms, and 2 * 6 = 12.

By cross multiplying, 3x = 36 and when we divide both sides by 3, we find x = 12.

Now that we know we have 12 7th graders, we can find the number of 6th graders. The process is similar with 7th graders on bottom, 6th graders on top, and x for what we do not know.

We went from 4 to 12 by multiplying 3 on the bottom, and we repeat it on the top. So 5 * 3 = 15.

Thus, there are 15 6th graders in the club.

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕