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Paha777 [63]
2 years ago
15

Sean is getting balloons for his grandfather's birthday party. He wants each balloon string to be 9 feet long. At the party stor

e, string is sold by the yard. If Sean wants to get 66 balloons, how many yards of string will he need?
Mathematics
1 answer:
atroni [7]2 years ago
3 0

Answer:

198 yards

Step-by-step explanation:

Sean wants the sting of each balloon to be 9 feet, and he wants to get a total of 66 balloons.

The total length of stings required for 66 balloons would be;

total length of balloon strings = 66 x 9 feet

                                                 = 594 feet

But the string is sold by the yard at the store.

So that,

1 yard = 36 inches = 3 feet

x yard = 594 feet

Thus,

x = \frac{594}{3}

  = 198 yards

x = 198 yards

Therefore, the total length of string that Sean would need is 198 yards.

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Solution :

Demand for cola : 100 – 34x + 5y

Demand for cola : 50 + 3x – 16y

Therefore, total revenue :

x(100 – 34x + 5y) + y(50 + 3x – 16y)

R(x,y)  = $100x-34x^2+5xy+50y+3xy-16y^2$

$R(x,y) = 100x-34x^2+8xy+50y-16y^2$

In order to maximize the revenue, set

$R_x=0, \ \ \ R_y=0$

$R_x=\frac{dR }{dx} = 100-68x+8y$

$R_x=0$

$68x-8y=100$  .............(i)

$R_y=\frac{dR }{dx} = 50-32x+8y$

$R_y=0$

$8x-32y=-50$  .............(ii)

Solving (i) and (ii),

4 x (i)    ⇒       272x - 32y = 400

     (ii)   ⇒   (-<u>)     8x - 32y = -50   </u>

                        264x        = 450

∴   $x=\frac{450}{264}=\frac{75}{44}$

     $y=\frac{175}{88}$

So, x ≈  $ 1.70      and    y = $ 1.99

    R(1.70, 1.99) = $ 134.94

Thus, 1.70 dollars per cola

          1.99 dollars per iced ted to maximize the revenue.

Maximum revenue = $ 134.94

4 0
3 years ago
Circular flower bed is 17 m in diameter and has a circular Samick around it is that to meters wide find the area of the sidewalk
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A= 8.5(3.14)

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If x is not an integer use the next smaller integer

[ 3.6 ] is not an integer, hence

[ 3.6 ] = 3

7 0
2 years ago
what number could be included in the data set 9,12,17,15,13 so the MEDIAN of the numbers in the set results in 14?
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<em><u>Your answer is 12,17,15,13 if you take out the 9 your median will be 14.</u></em>


~*"AUBA14"*~

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