SOLUTION: A and B make widgets. A and B together can finish making them in 24 days. A alone works for 16 days, then B alone works for 12 days. The rest of the widgets are 2/5 of the total. A

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Question 1163804: A and B make widgets. A and B together can finish making them in 24 days. A alone works for 16 days, then B alone works for 12 days. The rest of the widgets are 2/5 of the total. A makes 3 more widgets than B per day. How many widgets need to be made in total?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A and B make widgets. A and B together can finish making them in 24 days.
A alone works for 16 days, then B alone works for 12 days.
The rest of the widgets are 2/5 of the total. A makes 3 more widgets than B
per day. How many widgets need to be made in total?
Let the total number of widgets that need be made = n.
Let B's rate be x widgets/day.
Then A' rate is x + 3 widgets per day.

So in 24 days, B makes 24x widgets. 
And in 24 days, A makes 24(x + 3) widgets.
In 24 days, together they make n widgets.

24x+%2B+24%28x+%2B+3%29+=+n

When they work alone,
A makes 16(x+3) widgets
B makes 12x widgets 

Since the rest are 2/5 of n, working alone they made 3/5 of n 

16%28x+%2B+3%29%2B12x+=+expr%283%2F5%29n

system%2824x+%2B+24%28x+%2B+3%29+=+n%2C+16%28x+%2B+3%29+%2B+12x=+expr%283%2F5%29n%29

Solve that for x and n.

You finish.  The required answer will be the value of n.

Edwin

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of widgets produced each day by B; then the number produced by A each day is x+3.

A and B together can do the whole job in 24 days.

A working 16 days, and B working 12 days, can do 3/5 of the job (because 2/5 of the job remains to be done).

16%28x%2B3%29%2B12%28x%29+=+%283%2F5%29%2824%28x%2Bx%2B3%29%29
16x%2B48%2B12x+=+%283%2F5%29%2848x%2B72%29
28x%2B48+=+%28144%2F5%29x%2B%28216%2F5%29
28x%2B48+=+28.8x%2B43.2
4.8+=+0.8x
x+=+4.8%2F0.8+=+6

B produces 6 widgets a day; A produces 9.

Together in a day they produce 15 widgets.

Together they complete the job in 24 days, so the number of widgets is 24*15 = 360.