In Problem 10, if in the same amount of time that it takes her to read 40 pages of economics and 30 pages of sociology, Martha could read 20 pages of economics and 90 pages of sociology, then which of these equations describes combinations of pages of economics, E, and sociology, S, that she could read in the time it takes to read 40 pages of economics and 30 pages of sociology?
A) E + S = 110.
B) + S = 50.
C) 3E + S = 150.
D) E + S = 70.
E) All of the above.

Question

Quizplus · Accepted Answer

Let's use the information given to create two equations that relate the amount of pages Martha can read in the same amount of time:
40E + 30S = 20E + 90S
20E = 60S
S = 1/3 E

Now we can substitute this relationship into one of the equations given:
E + S = 110
E + 1/3 E = 110
4/3 E = 110
E = 82.5
S = 1/3 E = 27.5

Checking the other equations, we see that A, B, and D do not satisfy the 40E + 30S = 20E + 90S equation using the values we calculated for E and S. Therefore, the correct choice is C.

In Problem 10, If in the Same Amount of Time