Answered

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.


A.Let x represent the number of polyester-fill bags sold and let y represent the number of down-fill bags sold. Write a system of equations you can solve to find the number of each type sold.


B.Explain how you can solve the system for y by multiplying and subtracting.


C.Explain how you can solve the system for y using substitution.


D.How many of each type of bag were sold?

Verified Answer :

gvictorio

A.
x+y=14
79x+149y=1456

B.
-79(x+y=14)
79x+149y=1456

-79x-79y=-1106
79x+149y=1456
70y=350
y=350/70
y=5

79x+149(5)=1456
79x+745=1456
79x=1456-745
79x=711
x=711/79
x=9

C.
x=-y+14
79(-y+14)+149y=1456
-79y+1106+149y=1456
-79y+149y=1456-1106
70y=350
y=350/70
y=5

x=-y+14
x=-5+14
x=9

D.
9 polyester-fill
5 down-fill

Answer:

A.

x 79 + y149=1456

x +y = 14

B.

multiplying the second equation by 79 and subtracting it to the first equation.

C.

Solving for x in the second equation and Replacing x in the first equation, then solve for y.

D.

Down-fill sleeping bags(y) = 5

Polyester-fill sleeping bags (x) =9

Step-by-step explanation:

Hi, the sum of the product of each type of sleeping bag multiplied by its cost is equal to 1456 (equation1)

The sum of both sleeping bags sold is equal to 14 (equation 2)

A.

x 79 + y149=1456

x +y = 14

B. multiplying the second equation by 79 and subtracting it to the first equation.

79x + y149=1456

-

79x +79y = 1106

_____________

70y = 350

y = 350/70

y = 5

C. solving for x in the second equation:

x = 14-y

Replacing x in the first equation:

79 (14-y)+ 149y=1456

1106-79y +149y =1456

149y-79y = 1456-1106

70y =350

y = 350/70

y = 5

D:

Replacing the value of Y in any equation:

x +y = 14

x+ (5) =14

x =14-5

x = 9

Down-fill sleeping bags(y) = 5

Polyester-fill sleeping bags (x) =9