Represent these consecutive numbers (assuming that they are all integers):
x
x+1
x+2
x+3
x+4
x+5
and so on
x+8
x+9 is the tenth number. x+9 = 10, so x = 9.
Think of it this way: there are 10 consecutive numbers, and the last one is 10.
Working backwards, we get the sequence 10, 9, ... 3, 2, 1.
The sum of such an arith sequence is equal to the count of the numbers times the average of the first and last terms:
sum here = 10(1+10)/2 = 5(11) = 55 (answer)
t=D/r
Divide r by both sides to get t by itself.
The applicable formula is
A = P(r/12)/(1 -(1+r/12)^(-12n))
where P is the principal amount,
r is the annual interest rate (compounded monthly), and
n is the number of years.
Using the formula, we find
A = 84,400*(0.04884/12)/(1 -(1+0.04884/12)^(-12*15))
= 84,400*0.00407/(1 -1.00407^-180)
= 343.508/0.518627
≈ 662.34
The monthly payment on a mortgage of $84,400 for 15 years at 4.884% will be
$662.34
Lets say the number of adult tickets is x. This means the number of student tickets is 2x. So, 2x + x = 285, or 3x =285. The means x = 95. So the number of adult tickets sold is 95.
