Question

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 ?

Answer 1

Answer:

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:

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

So

$11y = 4z$

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

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

This means that:

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

$9x = 13y$

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

All of them is 100%

This means that:

$x + y + z = 1$

We need to find z.

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

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

Then

$x + y + z = 1$

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

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

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

$187z = 99$

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

$z = 0.5294$

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%.