SOLUTION: the fuel tank in a car was 40% full. i added 28 litres and then found it was 75% full. how much fuel does the tank hold?
instructions: form equations to solve this worded problem
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-> SOLUTION: the fuel tank in a car was 40% full. i added 28 litres and then found it was 75% full. how much fuel does the tank hold?
instructions: form equations to solve this worded problem
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Question 73352: the fuel tank in a car was 40% full. i added 28 litres and then found it was 75% full. how much fuel does the tank hold?
instructions: form equations to solve this worded problem Found 2 solutions by bucky, josmiceli:Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! Let x be the amount of gas the tank holds when full. Then all you need to do is write the
equation for the situation before you started. That situation was that the tank was 40% (decimal 0.4)
full.
.
So before you started you had 0.4*x litres in the tank representing 40% of a full tank.
.
Next you added 28 litres to that amount giving you what you started with plus 28 litres.
So now the tank has in it:
.
0.4*x + 28
.
But you then find that this amount is 75% (decimal 0.75) of a full tank. This can be written
as 0.75*x.
.
Set the two equal to get:
.
0.4x + 28 = 0.75*x
.
Subtract 28 litres from both sides to eliminate the 28 litres from the left side and get:
.
0.4*x = 0.75x - 28
.
Now subtract 0.75*x from both sides to eliminate the 0.75*x from the right side. This subtraction
results in:
.
-0.35*x = -28
.
Now just divide both sides by -0.35 and you find that:
.
x = -28/-0.35 = 80 litres
.
When the tank is full it contains 80 litres.
.
When you started the tank had 40% of 80 litres or it had 32 litres. You added 28 litres
and then the tank had 60 litres in it (32 plus 28). And this 60 litres was 75% or 3/4 of
a full tank. All the figures check, so it looks as if our answer is correct.
.
Hope this helps you to understand the problem a little better.
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