SOLUTION: 8) During a road trip, Tony drove one-third the distance that Lana drove. Mark drives 12 more miles than Lana drove. The total distance they drove on the trip was 369 miles. How m

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: 8) During a road trip, Tony drove one-third the distance that Lana drove. Mark drives 12 more miles than Lana drove. The total distance they drove on the trip was 369 miles. How m      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 944923: 8) During a road trip, Tony drove one-third the distance that Lana drove. Mark drives 12 more miles than Lana
drove. The total distance they drove on the trip was 369 miles. How many miles did each person drive?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = distance Tony drove
Let +b+ = distance that Mark drove
Let +c+ = distance that Lana drove
----------------------------------
(1) +a+=+%281%2F3%29%2Ac+
(2) +b+=+c+%2B+12+
(3) +a+%2B+b+%2B+c+=+369+
-----------------------
Substitute (1) and (2) into (3)
(3) +%281%2F3%29%2Ac+%2B+c+%2B+12+%2B+c+=+369+
(3) +c+%2B+3c+%2B+36+%2B+3c+=+1107+
(3) +7c+=+1071+
(3) +c+=+153+
and
(1) +a+=+%281%2F3%29%2Ac+
(1) +a+=+51+
and
(2) +b+=+c+%2B+12+
(2) +b+=+153+%2B+12+
(2) +b+=+165+
---------------------
Tony drove 51 mi
Mark drove 165 mi
Lana drove 153 mi
--------------------
check:
(3) +a+%2B+b+%2B+c+=+369+
(3) +51+%2B+165+%2B+153+=+369+
(3) +369+=+369+
OK