SOLUTION: Solve: to transport 60 tones of load a certain number of trucks were required. since the road was in bad condition each truck load was reduced by 0.5 ton . Therefore another 4 tru

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Question 132192: Solve: to transport 60 tones of load a certain number of trucks were required.
since the road was in bad condition each truck load was reduced by 0.5 ton . Therefore another 4 trucks werenecessary
to carry out this job.How many trucks were required originally?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t= the original number of trucks used
60%2Ft was the tons per truck
The problems says each truck load was reduced by 0.5 ton
60%2Ft+-+.5 is the adjusted load per truck
Four more trucks were needed
60%2Ft+-+.5+=+60%2F%28t%2B4%29
multiply both sides by t%28t%2B4%29
60%2A%28t%2B4%29+-+.5%2A%28t%2A%28t%2B4%29%29+=+60t
60t+%2B+240+-+.5%2A%28t%5E2+%2B+4t%29+=+60t
subtract 60t from both sides
240+-+.5t%5E2+-+2t+=+0
.5t%5E2+%2B+2t+-+240+=+0
multiply both sides by 2
t%5E2+%2B+4t+-+480+=+0
solve by completing the square
t%5E2+%2B+4t+%2B+%284%2F2%29%5E2+=+480+%2B+%284%2F2%29%5E2
%28t+%2B+2%29%5E2+=+484
t+%2B+2+=+22
t+=+20
Twenty trucks were required originally
check answer:
60%2Ft+-+.5+=+60%2F%28t%2B4%29
60%2F20+-+.5+=+60%2F%2820%2B4%29
3+-+.5+=+60%2F24
5%2F2+=+5%2F2
OK