Answer:
There are 585 adults and children
Step-by-step explanation:
Let the number of adults be a, number of children be c and the number of seniors be a
Amount made per group;
adults; 52 * a = 52a
Children : 26 * c = 26c
Seniors = 20 * s = 20s
Adding all will give 20,490
52a + 20s + 26c = 20 490 ••••(i)
Now let us work with the ratios;
a : s = 6 : 1
a/s = 6/1
a = 6s •••••(ii)
Lastly;
a/c = 4/9
4c = 9a ••••(ii)
We want to get a + c
From the first equation , let’s substitute
52(6s) + 20s + 26c = 20,490
26c = 6.5 (4c)
but 4c = 9a; 6.5(9a)
But a = 6s
So we have; 6.5(9)(6s) = 351s
so we have;
312s + 351s + 20s = 20,490
683s = 20,490
s = 20490/683
s = 30
Recall;
a = 6s = 6 * 30 = 180
4c = 9a
4c = 9 * 180
c = (9 * 180)/4 = 405
So the total number of children and adult is a + c
405 + 180 = 585
