SOLUTION: a company produces 3 kindes of envelopes Small Meduim Large. if the number of small envelope is 180, that of meduim is equal to number of small plus 5/6th of large, and that of

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Question 1038683: a company produces 3 kindes of envelopes Small Meduim Large. if the number of small envelope is 180,
that of meduim is equal to number of small plus 5/6th of large,
and that of large is equal to half of the number of small plus 3/7th of meduim
then wha is the number of meduim sized envelop produced, given that the total number is 4620 .
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Assign variables to the count of each envelope and transcribe the description into equations.

system%28x=small%2Cy=medium%2Cz=large%29

system%28x=180%2Cy=x%2B%285%2F6%29z%2Cz=%281%2F2%29x%2B%283%2F7%29y%29

Maybe next, try to simplify the system of equations.
system%28x=180%2C6y=6x%2B5z%2C14z=7x%2B6y%29
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system%286y=6%2A180%2B5z%2C14z=7%2A180%2B6y%29
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system%286y=1080%2B5z%2C14z=1260%2B6y%29
-
You can substitute to be able to first solve for z.
14z=1260%2B%281080%2B5z%29
14z=2340%2B5z
9z=2340
z=2340%2F9
highlight%28z=260%29-----Should be how many Large envelopes.

This solution has ignored the last part of the description, being the count of all envelopes to be 4620, but the system used should be enough to finish solving for x and y. Recall, x was already GIVEN as 180. This means, highlight%28x=180%29.

One of the system equations was 6y=6x+5z, or from earlier, y=x+(5/6)z;
y=180+(5/6)260
highlight%28y=396%262%2F3%29------this cannot be!


Some of the description is wrong, unless a mistake was made in this solution process.