Question

Central Middle School has 2,470 students and the ratio of students to teacher is 26:1. How many new teachers are needed to reduce this ratio to 19:1?

Answer 1

so, the school has 2470 students, and the ratio from students to teacher is 26:1 currently, so hmmm how many teachers are there with that ratio anyway?


`\bf \cfrac{student}{teacher}\qquad 26:1\implies \cfrac{26}{1}=\cfrac{\stackrel{2470}{students}}{\stackrel{teachers}{t}}\implies \cfrac{26}{1}=\cfrac{2470}{t} \\\\\\ t=\cfrac{1\cdot 2470}{26}\implies \boxed{t=95}`

hmm alrite... what if the amount of students is kept the same, but more teachers come in, that the ratio changes and is no longer 26:1 but 19:1?

how many teachers will there be then?


`\bf \cfrac{student}{teacher}\qquad 19:1\implies \cfrac{19}{1}=\cfrac{\stackrel{2470}{students}}{\stackrel{teachers}{t}}\implies \cfrac{19}{1}=\cfrac{2470}{t} \\\\\\ t=\cfrac{1\cdot 2470}{19}\implies \boxed{t=130}`

so, if there are 130 teachers and 2470 students, the ratio is 19:1.

at 26:1 is with 95 teachers.

how many more new teachers are needed? well, surely you'd know that.