widget maker increase production by six per day. She then can make 144 in four less days. What does she maker per day normally

Question

if a widget maker produces six more widgets per day than normally she can make 144 widgets in four less days. How many widgets does she make on a normal day 

 

Answer 1

Let W = number of widgets made on a normal day

Let D = number of days to normally make 144 widgets  

 

Note that W*D = 144  ==>  D = 144/W

 

If 6 more widgets per day then 144 widgets in 4 less days  ==>  

 

(W + 6)*(D - 4) = W*D = 144 

 

Substitute the value of D from the 1st equation into the 2nd equation 

 

(W + 6)*(144/W - 4) = 144

144 + 864/W - 4*W - 24 = 144

-4*W - 24 + 864/W = 0

-4*W^2 - 24*W + 864 = 0

W^2 + 6*W - 216 = 0

(W + 18)*(W - 12) = 0 

W = -18  or  W = 12

 

W cannot be negative so discard W = -18 

 

So W = 12 widgets made on a normal day 

 

Check:  12 widgets per day  ==>  12 days to make 144 widgets

            18 widgets per day  ==>  8 days to make 144 widgets