SOLUTION: A number of teachers were to receive 6 pens each but needed 4 more pens for them to be equally divided.if each teacher received 9 pens, 25 more pens would be necessary.how many pen

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Question 1011557: A number of teachers were to receive 6 pens each but needed 4 more pens for them to be equally divided.if each teacher received 9 pens, 25 more pens would be necessary.how many pens are there?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.
A number of teachers were to receive 6 pens each but needed 4 more pens for them to be equally divided.
If each teacher received 9 pens, 25 more pens would be necessary.how many pens are there?
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Let p = # of pencils, and n = # of teachers.

The first part of the condition says that   p +  4 = 6n.   (1)
The second part says that                   p + 25 = 9n.   (2)

Distract the first equation from the second one. You will get

25 - 4 = 3n,   or   n =  = 7.

Then from (1) you will get p = 6n - 4 = 6*7 - 4 = 42 - 4 = 38.

Answer. 7 teachers and 38 pens.


Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
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


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