Suppose A and B give the populations of two states where A > B. Compare the expressions and tell which of the given pair is greater or if the expressions are equal.

Question

b/a+b and 0.5

a + 13c and b + 13c, where c is the population of the third state

a - b/2 and a - b/2

a + b and 2b

5(a + b) and (a + b)5

Answer 1

population of state a > than population of state b

a) b/a+b and 0.5

Since a>b, b/a will be < 1. Thus b/a + b will be a bit more than b > 0.5 (States can't have fractional populations).

b) a + 13c and b + 13c, where c is the population of the third state

Adding 13c to both sides does not change the relation between a and b, so a+13c > b+13c

c) a - b/2 and a - b/2

These terms are equal to each other.

d) a + b and 2b

It is given that a>b so a+b > b+b = 2b

e) 5(a + b) and (a + b)5

5(a+b) = 5a+5b. (a+b)5 = a*5+b*5, but this equals 5a+5b. The two terms are equal.