3/5 of a class of students like strawberry ice-cream. 1/3 of the remaining students like chocolate ice-cream and the rest like vanilla ice-cream. Given that 28 more students like strawberry ice-cream than chocolate ice-cream, how many students like vanilla ice-cream?
ns = number of students like strawberry ice cream
nc = number of students like chocolate ice cream
nw = number of students like vanilla ice cream
nt = total number of students
Given:
ns = 3/5nt —> (1)
At 1/3 of the remaining students like chocolate ice cream
nc = 1/3 (nt - 3/5nt)
= nt/3 - nt/5
= nt (1/3 - 1/5)
nc = 2/5 nt
At given that 28 more students like strawberry ice cream than chocolate ice cream.
ns = 28 + nc
ns = 28 + 2/15nt —> (2)
Equate (1) to (2)
ns = ns
[3/5nt = 28 + 2/15nt]
Multiply both side by 15
[3/5nt = 28 + 2/15nt] (15)
9nt = 420 + 2nt
9nt - 2nt = 420
7nt = 420
nt = 420/7
nt = 60
solve for nv
nt = ns + nc + nv
nv = nt - ns - nc
nv = nt - 3/5nr - 2/15nr
nv = nt (1 - 3/5 - 2/15)
nv = nt (4/15)
nv = 60 (4/15)
nv = 16