400 algebra De mystif ieD
x () ()()( )
()
= ––^60 ± ^60 – ^41224 =^ ±
21
−^2603600 ––
= ± = ± =
896
2
60 2704
2
60 52
2
(^) , 45 6
(x = 56 is not likely to be a solution—the price would be $152!) If the price
of the shoes are 40 + 2(4) = $48 per pair, the revenue will be $3648.
More Work Problems
You might recall from Chapter 8 that we can solve work problems by filling in
the table below with information given in the problem. In the work formula
Q = rt (Q = quantity, r = rate, and t = time), Q is usually “1.” We then solve the
equation: Worker 1’s Rate + Worker 2’s Rate = Together Rate.
The information given in the problem is usually the time one or both work-
ers need to complete the job. We want the rates not the times. We can solve for
r in Q = rt to get the rates.
Q = rt
Q
t
=r
Because Q is usually “1,”^1
t
=r.
The equation to solve is usually:
111
Worker1’s time Worker2’s time Togetherti
+=
mme
Worker Quantity Rate Time
Worker 1 (^1) Worker s^11 , time
Worker 1’s time
Worker 2 1 1
Worker 2,s time
Worker 2’s time
Together (^1) Together^1 time^ Together time