Please help me with attached ration problem.Thanks
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We can plug in the answers, which represent the amount in January.The ratio of the amount of Alex's fuel oil bill for the month of February to the amount of his fuel oil bill for the month of January was 3/2. If the fuel oil bill for February had been $40 more, the corresponding ratio would have been 5/3. How much was Alex's fuel oil bill for January?
A. $240
B. $300
C. $360
D. $450
E. $540
Answer choice C: J=360.
3/2 = F/360
F = 540.
F+40 = 580.
580:360 = 29:18.
29:18 < 5:3.
Eliminate C.
The resulting ratio is too small.
The $40 being added to F needs to have more impact.
Thus, F and J have to be smaller.
To illustrate:
Let F=3000 and J=2000.
F+40 = 3040.
New F:J = 3040:2000. A very small increase in the ratio.
Let F=3 and J=2.
F+40 = 43.
New F:J = 43:2. A very big increase in the ratio.
Thus, to yield a bigger increase in the ratio, F and J must be smaller.
Eliminate D and E.
Answer choice B: J=300.
3/2 = F/300
F = 450.
F+40 = 490.
490:300 = 49:30.
49:30 < 5:3.
Eliminate B.
The correct answer is A.
For the curious, here's answer choice A:
3/2 = F/240
F = 360.
F+40 = 400.
New F:J = 400:240 = 5:3.
