A knitting shop orders yarn from three suppliers in Toronto

A knitting shop orders yarn from three suppliers in Toronto, Montreal, Ottawa. One month the shop ordered a total of 104 units of yarn from these suppliers. the delivery costs were $81, $53, $63 per unit for the orders from Toronto, Montreal, and Ottawa, respectively, with total delivery costs of $6386. The shop ordered the same amount from Toronto and Ottawa. How many units were ordered from each supplier?

units fromToronto=
units from Montreal=
units from Ottawa=

Solution

Let Toronto and Ottawa equal x and let Montreal equal M
shipping cost
81x+53x+65M=5990
solve for x
134x+63M=6386

let\'s make an expression for M
if they bought 104 units then
M+x+x=104
M+2x=104
M=104-2x
plug this into the answer from before

x=(6386-63(104-2x))/134
solve for x  
134x+-126X=166

X=20.75 = =21
they bought 21 units each from Toronto and Ottawa

from before
x+x+M=104
2x+M=104
2(21)+M=104
42+M=104
M=62
they bought 62 units from Montreal

21+21+62=104