<p>Martha is preparing for exams in economics and sociology. She has time to rea

Question

<p>Martha is preparing for exams in economics and sociology. She has time to read 40 pages of economics and 30 pages of sociology. In the same amount of time she could also read 30 pages of economics and 60 pages of sociology.<br /><br />Assuming that the number of pages per hour that she can read of either subject does not depend on how she allocates her time, how many pages of sociology could she read if she decided to spend all of her time on sociology and none on economics? (Hint: You have two points on her budget line, so you should be able to determine the entire line.)</p>

Explanation / Answer

Let us assume the total time to be t minutes. Let the rate of reading 1 page of economics be x min/page and sociology be y min/page. Then from the question we have, 40x+30y=t and 30x+60y=t we get, 40x+30y=30x+60y 10x=30y x=3y Now since the number of pages per hour that she can read of either subject does not depend on how she allocates her time. The pages of sociology she could read if she decided to spend all of her time on sociology and none on economics will be given by substituting x in terms of y and eliminating x from the equation. 40x+30y = t = 40*3y + 30y = 150y Hence she could read 150 pages of sociology and none of economics.

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