Question

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?

Answer 1

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.

$\frac{3}{2} = \frac{18}{x}$

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.

$\frac{5}{4} = \frac{x}{12}$

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 2

ANSWER
========

Ratio of 8th graders to 7th graders = 3 : 2

Let the number of graders be 3x and 2x

Number of 8th graders = 18

So , 3x = 18

x = 18/3 = 6

Number of 7th graders = 2 × 6 = 12

Ratio of 6th graders to 7th graders = 5 : 4

Let the number of graders be 5a and 4a

Number of 7th graders = 12

So , 4a = 12

a = 12/4 = 3

Number of 6th graders = 5×3 = 15 ANS

_______________________________

#BE BRAINLY