SOLUTION: a man has 105 $ and he wants to buy 13 items from market, each item costs 3$, 6$ and 12$, so how many items he can buy with 105$ find the amount of each item.

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Question 1117841: a man has 105 $ and he wants to buy 13 items from market, each item costs 3$, 6$ and 12$, so how many items he can buy with 105$ find the amount of each item.
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Quantity of each item x, y, z

system%28x%2By%2Bz=13%2C3x%2B6y%2B12z=105%29

system%28x%2By%2Bz=13%2Cx%2B2y%2B4z=35%29
Solution may contain more than one combination for x, y, z. You want whole-numbers only. First, assume that z is some already known or chosen constant; and solve for x and y. Find values for z which make sense, and find corresponding x or y for each.


If subtract item count equation from the simplified cost equation,
y%2B3z=22
Here, there will be very very few values for z which make any sense.
Go from there. Look at possible z values of Natural Numbers from 0 to 7 and see what happens to x and y.