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?
<pre>
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 + 24(x + 3) = 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(x + 3)+12x = expr(3/5)n}}}

{{{system(24x + 24(x + 3) = n, 16(x + 3) + 12x= expr(3/5)n)}}}

Solve that for x and n.

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

Edwin</pre>