A knitting shop orders yarn from three suppliers in Toronto, Montreal, and Ottaw

Question

A knitting shop orders yarn from three suppliers in Toronto, Montreal, and Ottawa. One month the shop ordered a total of 100 units of yarn from these suppliers. The delivery costs were $76, $47,and $57 per unit for the orders from Toronto, Montreal, and Ottawa, respectively, with total delivery costs of $5558.

The shop ordered the same amount from Toronto and Ottawa. How many units were ordered from each supplier? (Hint: "The shop ordered the same amount from Toronto and Ottawa." After getting an equation that describes this relationship, get all the variables to the same side of the equation.)

There were____ units ordered from Toronto, _____ units from Montreal, and______ units from Ottawa.

Explanation / Answer

Let Toronto and Ottawa equal x and let Montreal equal M
shipping cost
76x+57x+47M=5558
solve for x
133x+47M=5558
x=(5558-47M)/133

let's make an expression for M
if they bought 100 units then
M+x+x=100
M+2x=100
M=100-2x
plug this into the answer from before

x=(5558-47(100-2x))/133
solve for x
x=(5558-4700+94x)/133
x=(858+94x)/133
133x=858+94x
39x=858
x=22
they bought 22 units each from Toronto and Ottawa

from before
x+x+M=100
2x+M=100
2(22)+M=100
44+M=100
M=56
they bought 56 units from Montreal

22+22+56=100

76(22)+57(22)+47(56)=5558
133(22)+47(56)
2926+2632=5558

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