Raymond B. answered 01/21/22
Math, microeconomics or criminal justice
First shirt costs $20
if it reduces its cost by .10 = 10% for each additional shirt, that's the same as charging 1-.1 = 90% for each additional shirt. That seems to mean the costs are $20 + $20(.9) + $20(.9)^2 + $20(.9)^3 + ....+$20(.9)^n where n = the number of shirts
That's a geometric series whose sum = a1/(1-r) for an infinite number of shirts, with a1 =20 and r = common ratio = .9
sum = 20/(1-.9)= 20/.1 = $200 < $846. Even with an infinite number of shirts, the cost will be < $846
Possibly the cost is $84.6, not $846? The cost can't be $8.46, as $20>8.46
if total cost = $84.60 then
1 shirt costs $20
2 shirts cost 20 + .9(20) = $38
3 shirts cost 20+18+.9(18) = 38+16.2 = $54.2
4 shirts cost 54.2 + .9(16.2) = 54.2 + 14.58 = $68.78
5 shirts cost 68.78 + .9(14.58) = 68.78+ 13.122 = $81.902 which is close to $84.60
sum of a finite geometric sequence = S = a1(1-r^n)/(1-r) = 20(1-.9^n)/(1-.9) = 84.6
20(1.- 9^n) = 84.6(.1) = 8.46
1- .9^n = 8.46/20 = 4.23/10 = 0.423
.9^n = 0.577
.9^5 = 0.590 n= about 5 = the number of shirts
There's a mistake in the problem somewhere, a number wrong, or a decimal misplaced.