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