SOLUTION: The Randolphs used 12 more gal of fuel oil in October than in September and twice as much oil in November as in September. If they used 132 gal for the 3 months, how much was used

Question 76920: The Randolphs used 12 more gal of fuel oil in October than in September and twice as much oil in November as in September. If they used 132 gal for the 3 months, how much was used during each month
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The amount of fuel used each month is related to the amount used in September. So let's call
the unknown amount of fuel used in September S.
.
The problem then tells you that in October they used 12 more gallons than they did in September.
So in October they used S + 12 gallons.
.
Next the problem tells you that in November they used twice as much fuel as they did in
September. So in November they used 2*S.
.
Finally the problem tells you that the total used for these three months was 132 gallons. So
we can add up the usage for the three months and set that sum equal to 132 gallons. In
equation form this becomes:
.

.
On the left side combine all the terms that contain S to get:
.

.
Since we need to solve for S (the September usage), we need to get rid of the 12 on the
left side. Do this by subtracting 12 from both sides to get:
.

.
And finally we solve for S by dividing both sides by 4 to get:
.

.
So we know that in September they burned 30 gallons of fuel. In October we know that they
used 12 gallons more than they did in September. So in October they used 42 gallons.
And in November they used twice as much fuel as they did in September. So in November
they used 60 gallons of fuel.
.
Check: By month they used 30, 42, and 60 gallons of fuel. Total these up and see if the
total is 132 gallons ... because we know the total fuel used in those three months
is 132 gallons. If the total is 132, then we have correctly solved the problem because
all three requirements have been met ... 12 gallons more in October than in September,
twice as much used in November as in September, and a total usage of 132 gallons for the
three months.
.
Hope this helps you to understand the problem and see how you can develop a system for
solving it.
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