A company charges 20 to make one monogrammed shirt but reduc

A company charges $20 to make one monogrammed shirt, but reduces this cost by $0.10 per shirt for each additional shirt ordered up to 100 shirts. If the cost of an order is $917, how many shirts were ordered? If the cost of an order is $917. Shirts were ordered. (Simplify your answer.)

Solution

The cost goes like this,
$20, $19.9,$19.8,19.7 and so on

Total cost = $20 + $19.9 + $19.8 + 19.7 + .......
This is an arithmetic progression with a1 = 1 and d = -0.1
Total cost = n/2 [2a1 + (n-1)*d]
917 = n/2 * [2*20 + (n-1)*(-0.1)]
1834 = n*[40 -0.1*n + 0.1]
1834 = n*[40.1 -0.1*n]
0.1*n^2 - 40.1*n +1834 = 0
solving above quadratic equation we get,
n = 53 and n=348
but n should be less than 100
so,
n = 53
Answer: 53