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goldfiish [28.3K]

2 years ago

14

Reco noticed that a nearby store was selling skateboards 25% off. The original price of the skateboard he wanted was $68. He bou

ght the skateboard at the sale price. How much was his discount?

1 answer:

nexus9112 [7]2 years ago

6 0

He bought the skateboard at $51 it was $17 cheaper

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A concession stand at an athletic event is trying to determine how much to sell cola and iced tea for in order to maximize reven

Cerrena [4.2K]

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

The total revenue R earned (in dollars) from producing a gift box of candles is given by R(p)=-10p^2+800p, where p is the price

kherson [118]

A.) R(20) = -10(20)^2 + 800(20) = -10(400) + 16000 = -4000 + 16000 = $12,000

R(25) = -10(25)^2 + 800(25) = -10(625) + 20000 = -6250 + 20000 = $13,750

R(30) = -10(30)^2 + 800(30) = -10(900) + 24000 = -9000 + 24000 = $15,000

b.) For maximum revenue, dR/dp = 0
dR/dp = -20p + 800 = 0
20p = 800
p = 40

Therefore, the maximum revenue will be recorded when the price is set at $40.

4 0

3 years ago

Paula owns a shoe store in Los Angeles. Whenever she orders a new style of shoe, she orders 5 pairs of that style in each of the

suter [353]

She orders 5 pair in 5 different sizes:

5 x 5 = 25 pair

She orders 3 pair in 3 different sizes:

3 x 3 = 9 pair

Total pairs = 25 + 9 = 34 pair.

7 0

2 years ago

What is the value of x in the <br> triangle?

Makovka662 [10]

Answer:

x = 75°

Step-by-step explanation:

Sum of angles in a triangle: 180°

So,

50°+55°+x=180°

105°+ x = 180°

Subtract 105° from both sides

x = 75°

8 0

2 years ago

Timothy makes reduced copies of a photograph that has an actual length of 8 in. Each time he presses the reduce button on the co

Aleksandr-060686 [28]

Answer:

length of the photograph will be 4.2 in. after pressing the button 5 times.

Step-by-step explanation:

By pressing the button, every time size of the photograph gets reduced by 12%.

Therefore, the sequence formed by the reduced sizes of the photo will be a geometric sequence and the formula for the size of the reduced image will be,

L = $l(1-\frac{12}{100})^{n}$

Where l = Actual length of the photograph

L = length of the reduced image

n = Number of times the button has been pressed

For l = 8 in. and n = 5

L = $8(1-0.12)^{5}$

= $8(0.88)^{5}$

= 4.22 in

L ≈ 4.2 in.

Therefore, length of the photograph will be 4.2 in. after pressing the button 5 times.

3 0

3 years ago