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SIZIF [17.4K]
3 years ago
9

What are all of the values?

Mathematics
1 answer:
Arada [10]3 years ago
4 0

(i) x = 3

(ii) y = 6

<u>Explanation:</u>

The two polygons are similar.

The congruent angles are:

∠J ≅ ∠G

∠R ≅ ∠M

∠I ≅ ∠A

∠C ≅ ∠T

∠E ≅ ∠H

Proportional sides are:

\frac{JR}{GM} = \frac{RI}{MA} = \frac{IC}{AT} = \frac{CE}{TH} = \frac{EJ}{HG}

(i) Value of x = ?

\frac{JR}{GM} = \frac{RI}{MA}

Putting the values from the figure

\frac{6}{12} = \frac{2x + 1}{3x + 5} \\\\6 ( 3x + 5) = 12 ( 2x + 1)\\\\18x + 30 = 24x + 12\\\\30 - 12 = 24x - 18x\\\\18 = 6x\\\\x = 3

(ii) Value of y = ?

\frac{JR}{GM} = \frac{IC}{AT}

On putting the value we get:

\frac{6}{12} = \frac{x^2-4}{y+4} \\\\6(y+4) = 12(x^2 - 4)\\\\6y + 24 = 12[(3)^2 - 4]\\\\6y + 24 = 12[ 9 - 4]\\\\6y + 24 = 60\\\\6y = 36\\\\y = 6

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Step-by-step explanation:

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Then as per given,

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Selling price of one book = \$(\dfrac{330}{x-15})

Profit on each book= $1.50

Profit = selling price - cost price

\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}]

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Number of books cannot be negative.

So, there are 75 books.

Price of each book = \dfrac{300}{75}=\$4

So price of each book = $4.

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Answer:

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