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saw5 [17]
2 years ago
10

A used book store also started selling used CDs and videos. In the first week, the store sold 40 used CDs and videos, at 4.00 pe

r CD and 6.00 per video. The sales for both CDs and videos totaled to 180.00.
Mathematics
1 answer:
masha68 [24]2 years ago
4 0

Answer:

30 CDs and 10 Videos were sold.

Step-by-step explanation:

Given that a used book store also started selling used CDs and videos. In the first week, the store sold 40 used CDs and videos, at 4.00 per CD and 6.00 per video.

The sales for both CDs and videos totaled to 180.00.

Let CDs be x and Videos be y

Then we have x+y =3040

and 4x+6y = 180

Two simultaneous equations in two variables and can be solved by elimination method

multiply I equation by 4 and subtract from II.

2y = 20

y =10

x = 30

30 CDs and 10 Videos were sold.

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1/3 because there's more of the other marbles than red

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Huilan is 9 years younger than Thomas. The sum of their ages is 85. What is Thomas's age?
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The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much
Y_Kistochka [10]

Answer:

x = ∛ 2*V/5  

y = ∛ 2*V/5

h  = V/ ∛ 4*V²/25

Step-by-step explanation:

Dimensions of the aquarium base is  x*y

We call c₁ cost per unit area of the sides, then cost per unit area of slate is equal 5c₁.

let call h the height of the aquarium then volume of the aquarium is:

V = x*y*h      where   h =  V / x*y

As the base is a rectangular one there are 2 sides x*h .  and 2 sides  y*h

According to this:

Ct (cost of aquarium )  = cost of the base  + cost of the sides

cₐ  ( cost of the base) = 5*c₁*x*y

c₆ (cost of the sides ) = c₁*2*x*h   +   c₁*2*y*h

C(t)  =  5*c₁*x*y +2* c₁*x* V/x*y  +  2* c₁*y* V/x*y    or

C(t)  =  5*c₁*x*y  + 2*c₁*V/y   *2*c₁* V/x

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C´(x)  =  5*c₁*y - 2*c₁*V/x²

C´(y)  =  5*c₁*x - 2*c₁*V/y²

C´(x)  = C´(y)        ⇒  5*c₁*y - 2*c₁*V/x²  =   5*c₁*x - 2*c₁*V/y²

or    5*y - 2*V/x²  =   5*x - 2*V/y²

(5*y*x² - 2*V)/x²  = ( 5*y²x - 2*V) /y²

(5*y*x² - 2*V)*y²  = ( 5*y²x - 2*V)*x²

5*y³*x² - 2*V*y²  =  5*y²x³  - 2*V*x²

5*y³*x² - 5*y²x³  =  2*V * ( y² - x²)

by symmetry  x =  y

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C´(x) =  5*c₁*y - 2*c₁*V/x²

C´(x) =  5*c₁*x - 2*c₁*V/x²

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x = ∛ 2*V/5       and   y = ∛ 2*V/5    and   h  =  V/ x*y    h  = V/ ∛ 4*V²/25

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