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Marizza181 [45]
3 years ago
11

Two stores sell the same television for the same original price. Store A advertises that the television is on sale for 30% off t

he original price. Store B advertises that it is reducing the television’s price by $250. When Allison compares the sale prices of the television in both stores, she concludes that the sale prices are equal. Let p represent the television’s original price. Which equation models this situation?
Mathematics
2 answers:
prisoha [69]3 years ago
6 0

Answer: 0.7p = p-250

Step-by-step explanation:

Hi, to answer this question we have to write an equation using the information given:

For store A , it says that the television is on sale for 30% off the original price.So, in decimal form the percentage is 0.3 (30/100 =0.3), if we subtract 0.3 to 1  we obtain the percentage of the original price .

Store A  : 0.7 p

For store B, it advertises that it is reducing the television’s price by $250.So:

Store B : p -250

Where p is the television's original price.

To find the original price:

0.7p = p-250

Kamila [148]3 years ago
3 0
X*.70=250
X is the original price, x times .70, 70%, because it's 30% off, 250 should be the answer
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A manufacturer is planning to sell a new product at the price of 210 dollars per unit and estimates that if x thousand dollars i
sattari [20]

Answer:

Development costs: $2757

Promotion costs: $3155

Step-by-step explanation:

This might seem like a two-variable problem, but in actuality it's not - because the demand function is a sum of two components, each being independent and using only one variable, we can solve for the two separately.

Moreover, the price per unit and cost per unit is constant, so each product yields exactly $80 ($210 - $130).

Let's solve separately.

We need to maximize:

$80 * 160y/(y+4) - 1000y = $12800 * y/(y+4) - $1000*y

$80 * 170x/(x+7) - 1000x = $13600 * x/(x+7) - $1000*x

Let's go:

$12800 * y/(y+4) - $1000*y = $12800 * (1 - 4/(y+4)) - $1000y = $12800 - $51200/(y+4) - $1000*y

we analyze the derivative. $12800 is a constant, so we can skip it. Derivative of 1/(y+4) is -(y+4)^-2, derivative of $1000y is $1000.

deriv = $51200/(y+4)/(y+4) - $1000

We find the changepoints by analyzing $51200/(y+4)/(y+4) - $1000 = $0. We don't need to worry about y+4 = 0 because we cannot spend negative money on development/advertisement.

(y+4)^2 = $51.2

y+4 ~= 7.155417528 (or -y-4 = 7.1554... but it doesn't make sense because negative budget so we don't analyze).

y ~= 3.155417528

lastly, we should check that it's actually a maximum there - but it is, the original function goes to negative infinity.

rounding $1000y to the nearest dollar gives us $3155

Let's do the same for x:

$13600 * x/(x+7) - $1000*x = $13600 * (1 - 7/(x+7)) - $1000x = $13600 - $95200/(x+7) - $1000*x

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x ~= 2.75704...

rounding $1000x to the nearest dollar yields $2757

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