elliot drove 202.8 miles and used 6.5 gallons of gasoline.How many miles did he travel per gallon of gasoline?
2 answers:
Answer: The required number of miles traveled per gallon of gasoline is 31.2 miles.
Step-by-step explanation: Given that Elliot drove 202.8 miles and used 6.5 gallons of gasoline.
We are to find the number of miles that he traveled in one gallon of gasoline.
We will be using the UNITARY method o solve the given problem.
We have
Number of miles traveled in 6.5 gallon of gasoline = 202.8 miles.
Therefore, the number of miles that traveled in 1 gallon of gasoline is given by
Thus, the required number of miles traveled per gallon of gasoline is 31.2 miles.
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You have the right idea that things need to get multiplied.
What should be done is that the entire fraction needs to get multipled by the lowest common denominator of both denominators.
Let's look at the complex numerator. Its denominators are 5 and x + 6. Nothing is common with these, so both pieces are needed.
The complex denominator has x - 3 as its denominator. With nothing in common between it and the complex numerator, that piece is needed.
So we multiply the entire complex fraction by (5)(x + 6)(x -3).
Numerator:
= (x+6)(x-3) - (5)(5)(x-3)
= (x+6)(x-3) - 25(x-3)
= (x-3)(x + 6 - 25) <--- by group factoring the common x - 3
= (x -3)(x - 19)
Denominator:
Now we put the pieces together.
Our fraction simplies to (x - 3) (x - 19) / 125 (x + 6)