SOLUTION: To be able to fulfill one order of handicraft pieces given a deadline by the client,a team should make 25 pieces a day. After 3 days, the team increased the productivity by 5 piece

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Question 1141603: To be able to fulfill one order of handicraft pieces given a deadline by the client,a team should make 25 pieces a day. After 3 days, the team increased the productivity by 5 pieces and made 100 pieces over the plan based on the deadline. Find how many handicraft pieces the team made and how many days it took them.
Found 2 solutions by josmiceli, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = number of pieces they originally
needed to make by the deadline
+n%2F25+ is the number of days that would take
-------------------------
They made +3%2A25+=+75+ pieces in 3 days
In the remaining days, they made
+n+%2B+100+-+75+=+n+%2B+25+ pieces
at a rate of +30+ pieces per day
I can say:
+n%2F25+-+3+ is the number of remaining days
+30%2A%28+n%2F25+-+3+%29+=+n+%2B+25+
+%28+30%2F25+%29%2An+-+90+=+n+%2B+25+
+%28+6%2F5+%29%2An+-+n+=+115+
+%28+1%2F5+%29%2An+=+115+
+n+=+575+
They made +n+%2B+100+=+675+ pieces in
+n%2F25+=+575%2F25+
+n%2F25+=+23+ days
----------------------------------------------
check answer:
In 3 days they made +3%2A25+=+75+ pieces
There are +23+-+3+=+20+ days left
They need to make +675+-+75+=+600+ pieces in 20 days
at +30+ pieces/day
+30%2A20+=+600+
OK
Get a 2nd opinion if needed

Answer by ikleyn(52897) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let "n" be the number of days.


Then the condition says


    25*n + 100 = 25*3 + (25+5)*(n-3).


It is your equation to find n. 

Simplify it step by step :


    25n + 100 = 75 + 30(n-3)

    25n + 100 = 75 + 30n - 90

    100 - 75 + 90 = 30n - 25n

    115 = 5n

    n = 115%2F5 = 23.


ANSWER.  23 days and 25*23 = 575 pieces.

Solved.