Alan drives an average 100 miles each week .His car can travel an average of 25 miles per gallon of gasolines .Alan would to reduce his expenditure on gasoline by $\$5$
Which equation of the following can Alan use to determine how many fewer average miles ,m , he should drive each week ? Assuming that the gallon of gasoline costs $\$4$
$$a) \frac{25}{4}m = 95$$
$$ b) \frac{25}{4}m = 5$$
$$c)\frac{4}{25}m = 95$$
$$d) \frac{4}{25} m = 5$$
My turn : The cost of gasoline per week is $\$16$
So he wants to reduce the cost to be $\$11 $ per week
Then $$\frac{100}{16}= \frac{m}{11}= 68.75$$
But this answer does not math with any one of the choices
Find the average to reduce the expenditure
algebra-precalculus
Best Answer
In both (a) and (c) the only way to get "95" from the given data is to subtract 5 from 100. But "5" was the desired savings in dollars and 100 was the distance driven in miles. Subtracting dollars from miles is meaningless.
In (b) 25/4 is "miles per gallon" divided by "dollars per gallon" so "miles per dollar". The "5" on the right side is 5 dollars hoped to be saved. multiplying "miles per dollar" by m "miles" will not give "dollars".
In (d) 4/25 is "dollars per gallon" divided by "miles per gallon" so "dollars per mile". Here multiplying "dollars per mile" by m "miles" does give dollars! So this one is worth looking at. If he drives m miles and gets 25 miles per gallon, then he uses m/25 gallons. At 4 dollars per gallon that cost (4/25)m dollars. But that should be equal to the 16- 5= 11 dollars he wants to spend, not the 5 dollars he wants to save.
You are right. None of these is correct.m