My question is from OG 11th edition, page 166, question # 106. How do you do this problem?

Please post the problem text.

The present ratio of students to teachers at a certain school is 30 to 1. If the student enrollment were to increase by 50 students and the number of teachers were to increase by 5, the ratio of students to teachers would then be 25 to 1. What is the present number of teachers?

A. 5
B. 8
C. 10
D. 12
E. 15

THis is not a bad problem.


1. ------- S/T = 30/1

or S = 30T

2. ---------- (S+50)/(T+5) = 25/1

or (S+50) = 25T+125

from 1. ( 30T+50) = 25T+125

or T = 15

(E)

(Please verify the answer)

Yep, you got it. That's the algebraic way. You can also try the answer choices; choose whatever method is best for you.

If you try the answers, start with C (because they are in ascending order). If C) 10 is right, then there are currently 10 teachers. That would mean 30(10) = 300 students. Then the new numbers would be 300+50=350 students and 10+5=15 teachers, for a ratio of 350:15 or 70:3. Which isn't 25:1, so C is wrong. In addition, 70:3 is not quite high enough, so we can eliminate A and B; we need more teachers.

D) 12 = teachers, 360 = students now. 17 = teachers, 410 = students after. 410:17 doesn't simplify. Wrong.

E) 15 = teachers, 450 = students now. 20 = teachers, 500 = students after. 500:20 = 25:1. Bingo.

E is correct. Thank you for your help.