SOLUTION: An airplane begins a flight with a total of 136 litres of fuel stored in two separate wing tanks. During the flight 26.7% of the fuel in one tank is used. In the other tank, 45.6%

Algebra ->  Matrices-and-determiminant -> SOLUTION: An airplane begins a flight with a total of 136 litres of fuel stored in two separate wing tanks. During the flight 26.7% of the fuel in one tank is used. In the other tank, 45.6%       Log On


   



Question 716951: An airplane begins a flight with a total of 136 litres of fuel stored in two separate wing tanks. During the flight 26.7% of the fuel in one tank is used. In the other tank, 45.6% of the fuel is used. If 41 litres of fuel is used in total, find the amount of fuel (in litres) in each tank remaining at the end of the trip.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of fuel in 1st tank at beginning
Let +b+ = liters of fuel in 2nd tank at beginning
+.267a+ liters is used from 1st tank
+.456b+ liters is used from 2nd tank
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given:
(1) +a+%2B+b+=+136+
(2) +.267a+%2B+.456b+=+41+
------------------------
(2) +267a+%2B+456b+=+41000+
Multiply both sides of (1) by +267+
and subtract (1) from (2)
(2) +267a+%2B+456b+=+41000+
(1) +-267a+-+267b+=+-36312+
+189b+=+4688+
+b+=+24.8042+
and, since
(1) +a+%2B+b+=+136+
(1) +a+=+136+-+24.8042+
(1) +a+=+111.1958+
--------------------
+a+-+.267a+=+.733a+
+.733a+=+.733%2A111.1958+
+.733a+=+81.5065+
and
+b+-+.456b+=+.544b+
+.544b+=+.544%2A24.8042+
+.544b+=+13.4935+
---------------------
81.5065 liters is left in 1st tank
13.4935 liters is left in 2nd tank
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check answers
(2) +.267a+%2B+.456b+=+41+
(2) +.267%2A111.1958+%2B+.456%2A24.8042+=+41+
(2) +29.6893+%2B+11.3107+=+41+
(2) +41.0000152+=+41+
close enough