At haines elementary, 30% of the 120 teachers were male. the following school year, several new teachers were hired. the number of female teachers remained the same, but the number of males increased to 40%. how many new male teachers were hired? explain

So, at Haines Elementary there were 120 teachers.
Of these, 30% were male, so: 0.30*120=36 teachers were male.
Therefore there were 120-36=84 female teachers.
the following year more (male) teachers were hired, and now only 60% of teachers are female, so we have:

(60% is to 84 as 100% is to x)
Like this we find out that now there's a total of 140 teachers, instead of 120
So 20 new (male) teachers were added