# Math

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A manufacturer makes two products A and B, each of which is processed in two departments, production and finishing. Each A takes 3 hours to produce and six hours to finish, whereas each B takes 5 hours to produce and 2 hours to finish. How many units of A and B can be produced and finished if exactly 24 hours are available in each department and all hours must be used?

**I know the answer is 8 but i don't know how to do it and create the equation to get to that answer. **

• Math -

Let the number of A's be x
let the number of B's be y

for the production: 3x + 5y = 24
for the finishing : 6x + 2y = 24

double the first and subtract the 2nd
8y = 24
y = 3
sub back into the 1st:
3x + 15 = 24
x = 3

So they must make 3 A's and 3 B's

check: to product A takes 9 hours, to produce B takes 15 hours for a total of 24 in production.
to finish A takes 18 hrs, and it takes 6 hrs for B for a total of 24 hrs to finish.
my answer checks out.

I have not clue how or from where you got 8.
8 what? it makes no sense.

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