Impenetrable wrote:
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
I like to use two variables for these "changing ratios" questions.
The PRESENT ratio of students to teachers at a certain school is 30 to 1Let S = # of students PRESENTLY
Let T = # of teachers PRESENTLY
We can write: S/T = 30/1
Cross multiply to get: (1)(S) = (30)(T)
Simplify:
S = 30TIf 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 1In this scenario...
S + 50 = # of students
T + 5 = # of teachers
So, we get: (S + 50)/(T + 5) = 25/1
Cross multiply to get: (S + 50)(1) = (25)(T + 5)
Expand: S + 50 = 25T + 125
Simplify to get:
S = 25T + 75We now have 2 equations with 2 variables:
S = 30TS = 25T + 75To solve, replace
S in the bottom equation with
30TWe get:
30T =
25T + 75So: 5T = 75
Solve:
T = 15So, there are PRESENTLY
15 teachers
Answer: E
Cheers,
Brent
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