SOLUTION: Dave and bill each start saving today. Dave saves 30 cents per day. Bill saves 1 cent on the first day, 2 cents on the second day, 3 cents on the third day and so on saving one mor

Question 1031145: Dave and bill each start saving today. Dave saves 30 cents per day. Bill saves 1 cent on the first day, 2 cents on the second day, 3 cents on the third day and so on saving one more cent each day than on the day before. At the end of how many days will they have saved the same total amount?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let the number of days be x when they have saved the same amount
Dave saves 30x after x days
Bill saves 1 cent more everyday

1,2,3,4,......n
An Arithmetic sequence
Sx = x/2( 2+(x-1)1)
30x = x/2(2+(x-1))
60x =x(x+1)
x^2+x=60x
x+1=60
x=59 days
After 59 days they will have saved the same
CHECK
Dave => 30*59 = 1770
Bill => 59/2( 2+(59-1)1)
= 59/2(2+58)
= 59/2 * 60
= 59*60 =1770

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