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?

Answer: Hello!

so in the time Martha reads 40 pages of economics, and 30 pages of sociology, Martha also can read 10 pages of economics and 90 of sociology.

if we define E as the time needed for reading a page of economics, and S as the time needed to read a page of sociology then:

40*E + 30*S = time

10*E + 90*S = time

because the times are equal, you could write this:

40*E + 30*S = 10*E + 90*S

40*E - 10*E = 90*S - 30*S

30*E = 60*S

dividing by teen in both sides:

3*E = 6*S

E = (6/3) S = 2S

then in the time that martha reads one page of economics, she can read two pages of sociology.

Knowing that relation, you can see all the combinations of pages of S and E that Martha can read in the amount of time that she reads 40 pages of economics and 30 pages of sociology.

For example, if we took 10 pages of economics, you can read 20 pages of sociology in that time, then the combination is:

(40 - 10) = 30 pages of economics and (30 + 20) = 50 pages of sociology.