SOLUTION: A supply officer distributes 80 business envelops among 13 employees, giving half the number to the female employees and the other half to the male employees. Each female employee

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Question 949394: A supply officer distributes 80 business envelops among 13 employees, giving half the number to the female employees and the other half to the male employees. Each female employee received 3 more than each male. How many male employees are there?
Found 2 solutions by josgarithmetic, Theo:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
x females, y males, total 13 employees.
x%2By=13

Envelopes Per Type:
40%2Fx for females, 40%2Fy for males
because the 80 envelopes split into 40 and 40.

The description about how the envelopes among the gender types relate:
40%2Fx=3%2B40%2Fy
simplify to
40y=3xy%2B40x

Using total employee count substituting for y from it,
40%2813-x%29-40x-3x%2813-x%29=0
...doing the further simplification...
highlight_green%283x%5E2-119x%2B520=0%29

General solution method for a quadratic equation yields:
highlight%28x=5%29, highlight%28y=8%29.

Eight male employees.


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The solution process shown here was abbreviated, done thoroughly off-site.

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

you are given that the total number of employees are equal to 13.
you are also given that 80 envelopes are distributed among them, with 40 going to the males and 40 going to the females.
you are also given that each female employee receives 3 more than each male.

let x = number of males.
let y = number of females.
let a = number of envelopes that each male received.
let a+3 = number of envelopes that each female received.

since the males received 40 envelopes, and the number of envelopes each male received is equal to a, then a*x = 40

since the females received 40 envelopes, and the number of envelopes each female received is equal to a+3, then (a+3)*y = 40.

solve for x and solve for y in each of these equations to get both x and ys in terms of a.

you get:

a*x = 40 results in x = 40/a

(a+3)*y = 40 results in y = 40/(a+3)

you know that x+y = 13

replace x with 40/a and replace y with 40/(a+3) to get:

40/a + 40/(a+3) = 13

all you have to do now is solve for a.

multiply both sides of that equation by a*(a+3) to get:

40*(a+3) + 40*a = 13*a*(a+3)

simplify to get:

40a + 120 + 40a = 13a^2 + 39a

combine like terms to get:

80a + 120 = 13a^2 + 39a

subtract 80a from both sides of the equation and subtract 120 from both sides of the equation to get:

0 = 13a^2 + 39a - 80a - 120

combine like terms to get:

0 = 13a^2 - 41a - 120

flip sides in the equation to get:

13a^2 - 41a - 120 = 0

this is a quadratic equation in standard form.

factor it and you will get:

a = 5 or a = -24/13.

a can't be negative, so the solution is a = 5

in the formula of ax = 40, replace a with 5 to get 5x = 40 which results in x = 8.

in the formula of (a+3)y = 40, replace a with 5 to get 8y = 40 which results in y = 5.

number of males is 8
number of females is 5

8 males got 40 envelopes which results in 5 envelopes each.
5 females got 40 envelopes which results i 8 envelopes each.
each female got 3 more envelopes than each male.
problem is solved.

answer to the question is there are 8 male employees.