SOLUTION: the cost of renting a car co consists of a cost per day and a cost per kilometer. the cost of renting a car for 2 days and 150 km is 69. the cost of renting the same car for 3 days

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the cost of renting a car co consists of a cost per day and a cost per kilometer. the cost of renting a car for 2 days and 150 km is 69. the cost of renting the same car for 3 days      Log On


   

Question 1033165: the cost of renting a car co consists of a cost per day and a cost per kilometer. the cost of renting a car for 2 days and 150 km is 69. the cost of renting the same car for 3 days and 250 km is 108. what is cost per day
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = the cost / day
Let +b+ = the cost / km
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(1) +2a+%2B+150b+=+69+
(2) +3a+%2B+250b+=+108+
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(2) +a+%2B+%28250%2F3%29%2Ab+=+36+
(2) +a+=+%28-250%2F3%29%2Ab+%2B+36+
Substitute (2) into (1)
(1) +2%2A%28%28-250%2F3%29%2Ab+%2B+36%29+%2B+150b+=+69+
(1) +-500b+%2B+216+%2B+450b+=+207+
(1) +-50b+=+-9+
(1) +b+=+.18+
and
(2) +3a+%2B+250%2A.18+=+108+
(2) +3a+%2B+45+=+108+
(2) +3a+=+63+
(2) +a+=+21+
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The cost per day is $21
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check:
(1) +2%2A21+%2B+150%2A.18+=+69+
(1) +42+%2B+27+=+69+
(1) +69+=+69+
and
(2) +3%2A21+%2B+250%2A.18+=+108+
(2) +63+%2B+45+=+108+
(2) +108+=+108+
OK