Problema Solution
The ratio of student to teacher at Green School is 20:1. The ratio of student to teacher in the Blue School is 25:1. How many more teachers should Blue school hire to have the exact ratio as Green School?
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let
t = the number of teachers at Blue School
s = the number of students at Blue School
x = the number of teacher to hire
t : s = 25 : 1 cross-multiply
t = 25s
s = t/25
if the number of teacher is increased by x then there will be (t + x) teachers and the ratio will be:
(t+x) : s = 20 : 1 cross-multiply
t+x = 20s
plug s = t/25 into the last equation:
t + x = 20(t/25)
x = (20/25)t - t
x = t(4/5 - 1)
x = t(4/5 - 5/5)
x = -(1/5)t
this means that Blue school should decrease the number of teachers by 1/5.
let
t = the number of teachers at Blue School
s = the number of students at Blue School
x = the number of teacher to hire
t : s = 25 : 1 cross-multiply
t = 25s
s = t/25
if the number of teacher is increased by x then there will be (t + x) teachers and the ratio will be:
(t+x) : s = 20 : 1 cross-multiply
t+x = 20s
plug s = t/25 into the last equation:
t + x = 20(t/25)
x = (20/25)t - t
x = t(4/5 - 1)
x = t(4/5 - 5/5)
x = -(1/5)t
this means that Blue school should decrease the number of teachers by 1/5 of the current number of teachers.