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ohaa [14]
3 years ago
6

With an 18% discount, Joan was able to save $13.23 for a coat. What was the original price of the coat?

Mathematics
2 answers:
worty [1.4K]3 years ago
8 0

Answer:

The original price of the coat is $ 73.5

Step-by-step explanation:

Let x be the original price( in dollars ) of the coat.

Since, discount percentage = 18%,

Then  the amount of discount = 18% of x

=\frac{18x}{100}

According to the question,

\frac{18x}{100}=13.23

18x = 1323

\implies x =\frac{1323}{18}=73.5

Hence, the original price of the coat is $ 73.5.

irga5000 [103]3 years ago
3 0
P(18/100)=13.23

18p=1323

p=$73.50
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The relationship between the percentage of frozen citrus crop, and the cost of box of oranges is an illustration of a linear function.

  • <em>The linear equation of the function is: </em>g(P) =22.9P +7<em>, while its inverse is: </em>g^{-1}(c) = \frac{c - 7}{22.9}<em>.</em>
  • <em>The domain is from 0% to 100%, while the range is from 7 to 29.9</em>

<em />

Given that:

c = g(P)

<u>Input and Output quantity</u>

The input quantity is the <em>percentage of frozen citrus crop</em>, while the output quantity is the <em>cost of box of oranges</em>

<u>Linear Function</u>

The given parameters can be written as:

(P_1,c_1) = (20\%, 11.58)

(P_2,c_2) = (80\%, 25.32)

Calculate the slope (m)

m = \frac{c_2 - c_1}{P_2 - P_1}

So, we have:

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The equation is then calculated using:

c =m(P - p_1)  + c_1

So, we have:

c =22.9(P - 20\%)  + 11.58

c =22.9P - 4.58  + 11.58

c =22.9P +7

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g(P) =22.9P +7

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The domain is the <em>possible input value (i.e. possible values of P).</em>

Because P is a percentage, its possible values are 0% to 100%.

Hence, the domain of the function is: [0\%,100\%]

The range is the <em>possible output value (i.e. possible values of c).</em>

When P = 0% and 100%

c = 22.9 \times 0\% + 7 = 7

c = 22.9 \times 100\% + 7 = 29.9

Hence, the range of the function is: [7,29.9]

<u>The meaning of </u>g^{-1}(12)<u />

g^{-1}(12) is an inverse equation, where 12 represents the <em>cost of box of oranges.</em>

So, g^{-1}(12) represents the percentage of frozen citrus crop, when the cost is $12.

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We have:

c =22.9P +7

Make P the subject

22.9P = c - 7

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P = \frac{c - 7}{22.9}

So, the inverse function is:

g^{-1}(c) = \frac{c - 7}{22.9}

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<em />

g^{-1}(c) = \frac{c - 7}{22.9}

Substitute 12 for c

g^{-1}(12) = \frac{12 - 7}{22.9}

g^{-1}(12) = \frac{5}{22.9}

g^{-1}(12) = 22\%

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