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 10 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 = 70.
B) + S = 50.
C) 2E + S = 110.
D) E + S = 100.
E) All of the above.

Question

Quizplus · Accepted Answer

Let x be the amount of time it takes to read 40 pages of economics and 30 pages of sociology. From the problem, we know that:

40E/30S = 10E/90S

Solving for E/S, we get:

E/S = 9/4

This means that for every 9 pages of economics that Martha reads, she reads 4 pages of sociology. Let's say she reads E pages of economics and S pages of sociology in the same amount of time it takes to read 40 pages of economics and 30 pages of sociology. Then we can set up the following equation:

E + S = (40 + 30)(4/9) = 70/3

Multiplying both sides by 3, we get:

3E + 3S = 70

Simplifying, we get:

2E + S = 70

So the answer is (C).

In Problem 10, If in the Same Amount of Time