A knitting shop orders yarn from three suppliers in​ Toronto, Montreal, and Ottawa. One month the shop ordeblack a total of 103 units of yarn from these suppliers. The delivery costs were ​$80​,​$54​, and ​$60 per unit for the orders from​ Toronto, Montreal, and​ Ottawa, respectively, with total delivery costs of ​$6330. The shop ordeblack the same amount from Toronto and Ottawa. How many units were ordeblack from each​ supplier? (Hint:​ "The shop ordeblack 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.) units ordeblack from Toronto units ordeblack from Montreal units ordeblack from Ottawa

Rishi Hale

Rishi Hale

Answered question

2022-07-27

A knitting shop orders yarn from three suppliers in​ Toronto, Montreal, and Ottawa. One month the shop ordeblack a total of 103 units of yarn from these suppliers. The delivery costs were ​$80​,​$54​, and ​$60 per unit for the orders from​ Toronto, Montreal, and​ Ottawa, respectively, with total delivery costs of ​$6330. The shop ordeblack the same amount from Toronto and Ottawa. How many units were ordeblack from each​ supplier? (Hint:​ "The shop ordeblack 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.)
___ units ordeblack from Toronto
___ units ordeblack from Montreal
___ units ordeblack from Ottawa

Answer & Explanation

Jazlene Dickson

Jazlene Dickson

Beginner2022-07-28Added 15 answers

Given that the shop ordeblack the same amount from Toronto and Ottawa
Let number of units ordeblack from Toronto = x
Hence, number of units ordeblack from Ottawa will also be equal to = x
Let, number of units ordeblack from Montreal = y
The shop ordeblack a total of 103 units of yarn from these suppliers
Hence, x+x+y = 103
=> 2x+y=103 ..........................(1)
The delivery costs were ​$80​, ​$54​, and ​$60 per unit for the orders from​ Toronto, Montreal, and​ Ottawa, respectively, with total delivery costs of ​$6330
Hence, 80x+60x+54y = 6330
=> 140x+54y = 6330 ..................(2)
Multiply equation (1) by 54 and subtract from equation (2):
140x-54 * 2x+54y-54 * y = 6330-103 * 54
=> 32x =768
=> x=24
Substituting the value of x in equation (1) we get,
2x+y = 103
=> 2 \times 24+y = 103
=> y = 103-48=55
Hence,
24 Units ordeblack from Toronto
55 Units ordeblack from Montreal
24 Units ordeblack from Ottawa

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