Question

A knitting shop orders yarn from three suppliers in Toronto, Montreal, and Ottawa. One month the shop ordered total of 101 units of yarn from
these suppliers. The delivery costs were $80, $50, and $62 per unit for the orders from Toronto, Montreal, and Ottawa, respectively, with total delivery costs of $6100. The shop ordered the same amount from Toronto and Ottawa. How many units were ordered from each supplier?

Answer 1

Let Toronto and ottawa equal x and let Montreal equal M

shipping cost

80x+62x+50M=6100

solve for x

142x+50M=6100

x=(6100-50M)/142 --------------Eq(i)

Lets make an Expression for M

if they bought 101 units then

M+x+x=101

M+2x=101

M=101-2x

subtitute in above Equation---------(i)

x=(6100-50(101-2x)) / 142

x=(6100-5050+100x) / 142

142x=(1050+100x)

42x=1050

x=25

They bought 25 units each from Toronto and ottawa

From before

x+x+M=101

2x+M=101

2(25)+M=101

50+M=101

M=51

They bought 51 units from Montreal

[ Check it:25+25+51=101]

80(25)+50(51)+62(25)=6100

2000+2550+1550=6100

Therefore 6100=6100