SOLUTION: The Nelson family has discovered that the cost C of their family vacation is a constant k times the length d, in days, of the vacation added to the cost t of transportation to get

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Question 511789: The Nelson family has discovered that the cost C of their family vacation is a constant k times the length d, in days, of the vacation added to the cost t of transportation to get to and from their vacation spot, as shown by the function C(d) = kd + t. The Nelson family had to shorten their planned vacation by 3 days. How much less did the shortened vacation cost than the original planned vacation?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Their original vacation was
+C%28d%29+=+k%2Ad+%2B+t+
Their shortened vacation was
+C%28d-3%29+=+k%2A%28d-3%29+%2B+t+
The difference in cost is
+C%28d%29+-+C%28d-3%29+=+k%2Ad+%2B+t+-+k%2A%28d-3%29+-+t+
+C%28d%29+-+C%28d-3%29+=+k%2Ad+-+k%2Ad+%2B+3k+
+C%28d%29+-+C%28d-3%29+=+3k+
check:
Suppose
+k+=+11+
+d+=+9+
+t+=+17+
+C%289%29+=+11%2A9+%2B+17+
+C%289%29+=+116+
and
+C%289-3%29+=+11%2A%289-3%29+%2B+17+
+C%286%29+=+66+%2B+17+
+C%286%29+=+83+
and
+C%289%29+-+C%286%29+=+116+-+83+
+C%289%29+-+C%286%29+=+33+
+k+=+11+
+3k+=+33+
OK