Question 1011557
let p = number of pens.
lex x = number of teachers.


for each teacher to get 6 pens, 4 more pens would be required.


this means that the number of pens available is equal to 6x - 4.


for each teacher to get 9 pens, 25 more pens would be required.


this means that the number of pens available is equal to 9x - 25.


you have 2 equations.


p = 6x - 4
p = 9x - 25


in both equations, the value of p and the value of x needs to be the same because the number of pens is the same in both equtions and the number of teachers is the same in both equations.


if you subtract the first equation from the seecond equation, you wind up with.


0 = 3x - 21


this is because:
p minus p = 0
9x - 6x = 3x
-25 - (-4) = -25 + 4 = -21


add 21 to both sides of the equationt to get:


21 = 3x


divide both sides of the equation by 3 to get:


7 = x


that tells you that the number of teachers has to be equal to 7.


now that you know the number of teachers, you can solve for the number of pens in each equation.


p = 6x - 4 becomes p = 42 - 4 which becomes p = 38


p = 9x - 25 becomes p = 63 - 25 which becomes p = 38.


you're done.


the number of pens available is 38.
the number of teachers is 7.


they tried to give each of the 7 teachers 6 pens and came up short 4 because they required 42 pens but only have 38.


42 - 38 = 4


they tried to give each of the 7 teachers 9 pens and came up short 25 because they required 63 pens but only have 38.


63 - 38 = 25