Explanation:
well, we have already the equation.
for any true statement, when we use its numbers, the equation has to stay true.
if not then the statement is wrong too.
240 = 12x + 8y
x = number of adults
y = number of children
A.
no adults means x = 0
240 = 8y
y = 30
so, yes, true, without adults there could be 30 children.
B.
10 students (children), y = 10
240 = 12x + 8×10 = 12x + 80
160 = 12x
x = 160/12 = 40/3 = 13.3333...
no, there can be max. 13 adults (not 15).
C.
240 = 12(x + 4) + 8(y - 6) = 12x + 48 + 8y - 48 = 12x + 8y
that is still the same equation as before.
so, yes, this is true.
D.
240 = 12(x - 3) + 8(y + 2) = 12x - 36 + 8y + 16 = 12x + 8y - 20
260 = 12x + 8y
with 2 students less and 3 teachers more costs $260, and therefore more than the budget.
so, no, this is not true.
E.
the picture is very fuzzy. does this mean 16 adults and 6 children ?
240 = 12×16 + 8×6 = 192 + 48 = 240
so, yes, this is true.