This weekend, Martha has time to read 40 pages of economics and 30 pages of sociology. Alternatively, she could read 30 pages of economics and 50 pages of sociology. Which of these equations describes all combinations of pages of economics, E, and sociology, S, that she could read over the weekend?
A) E + S = 70.
B) E/2+S=50
C) 2E + S = 110.
D) E + S = 80.
E) All of the above.

Question

Quizplus · Accepted Answer

We can set up the following system of equations:
Economics + Sociology = Total Pages Read
40 + 30 = 70
30 + 50 = 80
We can then solve for E by subtracting S from both sides:
E + S = 70
E = 70 - S
E + 2S = 80
E = 80 - 2S
Setting these two equations equal to each other, we get:
70 - S = 80 - 2S
Solving for S, we get:
S = 10
Substituting this value of S back into either equation, we get:
E = 60
Therefore, the equation that describes all possible combinations of pages of economics and sociology is 2E + S = 110, and the answer is C.

This Weekend, Martha Has Time to Read 40 Pages of Economics