(PLEASE HELPP) The number of 6th graders in RSM summer camp to that of 7th graders was 4 to 11, while the number of 5th graders to that of the 6th graders was 13 to 9. By what percent did the number of 7th graders exceed that of the number of 5th and 6th graders taken together ?

The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.

Step-by-step explanation:

I am going to say that:

x is the proportion of 5th graders.

y is the proportion of 6th graders.

z is the proportion of 7th graders.

The number of 6th graders in RSM summer camp to that of 7th graders was 4 to 11

This means that:

\frac{y}{z} = \frac{4}{11}

z

y

=

11

4

So

11y = 4z11y=4z

y = \frac{4z}{11}y=

11

4z

The number of 5th graders to that of the 6th graders was 13 to 9.

This means that:

\frac{x}{y} = \frac{13}{9}

y

x

=

9

13

9x = 13y9x=13y

x = \frac{13y}{9}x=

9

13y

All of them is 100%

This means that:

x + y + z = 1x+y+z=1

We need to find z.

y = \frac{4z}{11}y=

11

4z

x = \frac{13y}{9} = \frac{13*4z}{9*11} = \frac{52z}{99}x=

9

13y

=

9∗11

13∗4z

=

99

52z

Then

x + y + z = 1x+y+z=1

\frac{52z}{99} + \frac{4z}{11} + z = 1

99

52z

+

11

4z

+z=1

The lcm(least common multiple) between 11 and 99 is 99. Then

\frac{52z + 9*4z + 99z}{99} = 1

99

52z+9∗4z+99z

=1

187z = 99187z=99

z = \frac{99}{187}z=

187

99

z = 0.5294z=0.5294

By what percent did the number of 7th graders exceed that of the number of 5th and 6th graders taken together ?

z(7th graders) is 52.94%.

x + y(5th and 6th graders) is 100 - 52.94 = 47.06%

52.94 - 47.06 = 5.88

The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.