Direction : Read the data given below carefully and answer the questions.…

Concept

In two-variable word problems, translate each English statement into an algebraic equation using clearly defined variables, then solve the system. Two relations in two unknowns determine a unique solution, and any extra condition given must be used as a check or to pin down the remaining unknown.

Application

Let the number of girls in school A be g and the number of boys in school A be b. Translate the statements:

1. Girls in B exceed twice the girls in A by 30, and girls in B = 450, so 2g + 30 = 450, giving g = 210.

2. Boys in B equal the total students in school A, so boys in B = b + g = b + 210.

3. Total students in B = girls in B + boys in B = 450 + (b + 210) = b + 660.

4. The extra condition: total in B is 180 less than twice the total in A, i.e. b + 660 = 2(b + 210) − 180.

5. Solve: b + 660 = 2b + 420 − 180 = 2b + 240, so b = 420 (boys in A).

6. Therefore total students in A = b + g = 420 + 210 = 630, and boys in B = total students in A = 630.

Cross-check

With boys in A = 420 and girls in A = 210, total in A = 630 and total in B = 450 + 630 = 1080. Check the extra condition: twice the total in A minus 180 = 2 × 630 − 180 = 1260 − 180 = 1080, which matches total in B. The result 630 is consistent.