At a sports carnival,the ratio of number of pupils sent by school A,B and school C to the event was 1:2:3. The number of boys from school A and the number of girls from school B were the same. The ratio of the number of girls from school C to the total number of girls was 7:10. There were 124 fewer boys than girls altogether.

Question

(a) What was the ratio of the number of boys from school C to the total number of boys?
(b) What was the total number of girls at the carnival? ( express your answer in the simplest form)

Answer 1

students from A -- x
students from B -- 2x
students from C -- 3x
total students = 6x

girls from C --- 7y
total girls ------ 10y

total boys ------ 6x-10y
"There were 124 fewer boys than girls altogether"
---> girls - boys = 124
---> 10y - (6x-10y) = 124
20y - 6x = 124
10y - 3x = 62
10y = 62+3x , clearly 62+3x must be a multiple of 10
possible cases: x must end in 6
x=6 , y = 8
students from A = 6
students from B = 12
students from C = 18
total students = 36
total girls = 80
total boys = 36-80 = -44 ---- Fail

x = 16, y = 11
students from A = 16
students from B = 32
students from C = 48
total students = 96
total girls = 110
total boys = 96-110 = -14 ---- Fail

x = 26 , y = 14
students from A = 26
students from B = 52
students from C = 78
total students = 156
total girls = 140
total boys = 156-140 = 16 ---- Fail, not a difference of 124

x = 36 , y = 17
students from A = 36
students from B = 72
students from C = 108
total students = 216
total girls = 170
total boys = 216-170 = 46 ---- Fail

x = 46 , y = 20
students from A = 46
students from B = 92
students from C = 138
total students = 276
total girls = 200
total boys = 276-200 = 76 ---- Fail

x = 56 , y = 23
students from A = 56
students from B = 112
students from C = 168
total students = 336
total girls = 230
total boys = 336-230 = 106 ---- Fail

etc

cute little program, to show the extension of this

10 for x = 6 to 106 step 10
20 y = (62+3*x)/10
30 if 6*x-10*y = 124 then end
40 print x,y,6*x-10*y
50 next x
>run
6 8 -44
16 11 -14
26 14 16
36 17 46
46 20 76
56 23 106
66 26 136
76 29 166
86 32 196
96 35 226
106 38 256
>

looks like there are no values that satisfy your conditions