HELP WITH THREE QUESTIONS PLS

One-third of the people from country a claim that they are from country b, and the rest admit they are from country a. one-fourth of the people from country claim that they are from country a, and the rest admit they are from country b. in a combined census of the two countries, one-half of the total claimed to be from a. what is the ratio of the populations of country a to that of country b.

Liz had 140 pens and inna had 100 pens. after inna gave liz some pens, liz had 3 times as many pens as inna. how many pens did inna give liz?

What is the missing reason in the proof? segment addition congruent segments theorem transitive property of equality subtraction property of equality?