SOLUTION: If im doing a marathon for charity and every mile i run i earn 16$ every mile i bike i earn 12$. At the end of the marathon i ran and biked a total of 24 miles and earned 318$. How

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: If im doing a marathon for charity and every mile i run i earn 16$ every mile i bike i earn 12$. At the end of the marathon i ran and biked a total of 24 miles and earned 318$. How      Log On

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Question 955181: If im doing a marathon for charity and every mile i run i earn 16$ every mile i bike i earn 12$. At the end of the marathon i ran and biked a total of 24 miles and earned 318$. How many miles did i run and how many miles did i bike?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Ler +r+ = number of miles you run
Let +b+ = number of miles you bike
-----------------
(1) +r+%2B+b+=+24+
(2) +16r+%2B+12b+=+318+
------------------------
Multiply both sides of (1) by +12+
and subtract (1) from (2)
(2) +16r+%2B+12b+=+318+
(1) +-12r+-+12b+=+288+
-----------------------
+4r+=+30+
+r+=+7.5+
and, since
(1) +r+%2B+b+=+24+
(1) +7.5+%2B+b+=+24+
(1) +b+=+16.5+
-----------------
7.5 = number of miles you run
16.5 = number of miles you bike
------------
check:
(2) +16r+%2B+12b+=+318+
(2) +16%2A7.5+%2B+12%2A16.5+=+318+
(2) +120+%2B+198+=+318+
(2) +318+%2B+318+
OK