At raging river sports, polyester fill sleeping bags sell for $79. Down fill sleeping bags sell for $149. In one week the store sold 14 sleeping bags for $1456. How many of each were sold using system of equation multiplying and subtracting.

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absor201 absor201 · Answer 1 · 2019-11-26T10:37:01+01:00

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

[tex]79(x+y=14)\\79x+79y=1106\ \ \ Eqn 3\\[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](79x+149y)-(79x+79y)=1456-1106\\79x+149y-79x-79y=350\\70y=350[/tex]

Dividing both sides by 70

[tex]\frac{70y}{70}=\frac{350}{70}\\y=5[/tex]

Putting y=5 in Eqn 1

[tex]x+5=14\\x=14-5\\x=9\\[/tex]

9 Polyester fill and 5 down fill sleeping bags were sold.

Keywords: Linear equations, subtraction

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