9 Polyester fill and 5 down fill sleeping bags were sold.
Step-by-step explanation:
Let,
Polyester fill sleeping bags = x
Down fill sleeping bags = y
Price of 1 polyester fill bag = $79
Price of 1 down fill bag = $149
According to given statement;
x+y=14 Eqn 1
79x+149y=1456 Eqn 2
Multiplying Eqn 1 by 79
![79(x+y=14)\\79x+79y=1106\ \ \ Eqn 3\\](https://tex.z-dn.net/?f=79%28x%2By%3D14%29%5C%5C79x%2B79y%3D1106%5C%20%5C%20%5C%20Eqn%203%5C%5C)
Subtracting Eqn 3 from Eqn 2
![(79x+149y)-(79x+79y)=1456-1106\\79x+149y-79x-79y=350\\70y=350](https://tex.z-dn.net/?f=%2879x%2B149y%29-%2879x%2B79y%29%3D1456-1106%5C%5C79x%2B149y-79x-79y%3D350%5C%5C70y%3D350)
Dividing both sides by 70
![\frac{70y}{70}=\frac{350}{70}\\y=5](https://tex.z-dn.net/?f=%5Cfrac%7B70y%7D%7B70%7D%3D%5Cfrac%7B350%7D%7B70%7D%5C%5Cy%3D5)
Putting y=5 in Eqn 1
![x+5=14\\x=14-5\\x=9\\](https://tex.z-dn.net/?f=x%2B5%3D14%5C%5Cx%3D14-5%5C%5Cx%3D9%5C%5C)
9 Polyester fill and 5 down fill sleeping bags were sold.
Keywords: Linear equations, subtraction
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