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? With steps please.
a. E+S = 70
b. E/2+S = 50
c. 2E+S = 110
d. E+S = 20
e. All of the above.

a,b and c.

Explanation:

E= Economics

S= Sociology

From statement 1,

E= 40

S= 30

E+S = 40+30

Thus, E+S = 70

Hence, option "a" is a possible combination.

From statement 1 also,

E/2 + S = (40/2) + 30 = 20+30=50

Hence option "b" is correct.

From statement 2,

E= 30

S = 50

E+S = 30+ 50 = 80

2E + S =(2×30) + 50 = 60+50=110

Thus, "c" is correct.

for option d

E+ S = 20 will be tested using statements 1 and 2 separately.

Using statement 1,

E+S = 30+40=70 which is not equal to 20. Hence option "d" is wrong.

Also, using statement 2,

E+S = 30+50= 80 which is not equal to 20. Hence option d fails to satisfy statement 2.

Hence the equations that describe possible combination of pages of Economics and Sociology are equations a, b, and c.

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