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2 years ago

An article reports Sales have grown by 30% this year to $200 million, what were sales before the growth?

Mathematics

1 answer:

Varvara68 [4.7K]2 years ago

8 0

Answer:

Price before growth = $ 153.85 million

Step-by-step explanation:

Given:

Percentage = 30%

Rate after Increase =new value= $200 million

To Find:

Sales before growth =old value= ?

Solution:

We Know the formula for Percentage growth which is given by the formula

Percentage growth $= \frac{Difference value}{old value}*100$ %

Now let old value = x

Difference = New Value - x

= 2000 - x

We have formula

Percentage growth $= \frac{Difference value}{old value}*100$ %

Putting in values

30 % $= \frac{Difference value}{old value}*100$ %

30 $= \frac{Difference value}{old value}*100$

Putting in values

30 $= \frac{200-x}{x}*100$

multiplying both sides by x

it becomes

30 x = (200-x)*100

Multiplying inside

30 x = 20000 - 100 x

Adding 100 x on both sides

30 x + 100 x = 20000 - 100 x + 100 x

it becomes

130 x = 20000

Dividing both sides by 130

$\frac{130*x}{130}=\frac{20000}{130}$

itgives us

x = $ 153.85 million

Price before growth = $ 153.85 million

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We shall solve this by using the elimination method, since none of the variables has a coefficient of 1. We'll start by multiplying equation (1) by 3 and multiplying equation (2) by 2 (so as to eliminate the m variable)

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2 years ago

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Step-by-step explanation:

Given:

$\angle DBC=40$ °

From the triangle, using the theorem that center angle by an arc is twice the angle it subtend at the circumference.

$m\textrm{ arc CD}=2\times \angle DBC\\m\textrm{ arc CD}=2\times 40=80$

Also, the diameter of the circle is BD. As per the theorem that says that angle subtended by the diameter at the circumference is always 90°,

$m\angle BCD=90$

From the Δ BCD, which is a right angled triangle,

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Now, using the theorem that angle between the tangent and a chord is equal to the angle subtended by the same chord at the circumference.

Here, chords CD and BC subtend angles 40 and 50 at the circumference as shown in the diagram by angles $m\angle DBC\textrm{ and }m\angle BDC$ and EF is a tangent to the circle at point C.

Therefore, $m\angle DCF=m\angle DBC=40\\m\angle ECB=m\angle BDC=50$

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$m\angle DCF=50\\\therefore m\textrm{ arc BC}=2\times m\angle DCF=2\times 50=100$

Hence, all the angles are as follows:

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2 years ago

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