Question

The product of five numbers is ( -77760 ) .if four of these numbers are -6, -9, -12 and 15 . find the fifth number​

Answer 1

Step-by-step explanation:

Let the fifth no bex

then;

-6*-9*-12*-15*x = -77760

-9720x= -77760

x =8

Answer 2

• The fifth number = 8.

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Given :

• The product of five numbers = –77760.
• The four numbers = –6, –9, –12 and 15.

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To Find :

• The fifth number.

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Solution :

Let,

The fifth number be x.

According to the question,

The product of five numbers is –77760.

I.e.,

First number × Second number × Third number × Fourth number × Fifth number = –77760

We have,

• First number = –6.
• Second number = –9.
• Third number = –12.
• Fourth number = 15.

$\implies ( - 6) \times ( - 9) \times ( - 12) \times 15 \times x = - 77760$

$\implies 54 \times ( - 180) \times x = - 77760$

$\implies - 9720 \times x = - 77760$

$\implies x = \dfrac{ \cancel- 7776 \cancel0}{ \cancel - 972 \cancel0}$

$\implies x = \cancel\dfrac{7776}{972}$

$\implies x = \cancel\dfrac{3888}{486}$

$\implies x = \cancel\dfrac{1944}{243}$

$\implies x = \cancel \dfrac{648}{81}$

$\implies x = \cancel\dfrac{216}{27}$

$\implies x = \cancel \dfrac{72}{9}$

$\implies x = \cancel \dfrac{24}{3}$

$\implies x = \dfrac{8}{1}$

$\implies x = 8$

Hence,

The fifth number is 8.

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Verification :

The product of five numbers is –77760

Now we have,

• First number = –6.
• Second number = –9.
• Third number = –12.
• Fourth number = 15.
• Fifth number = 8.

$\implies (-6) \times (-9) \times (-12) \times 15 \times 8 = -77760$

$\implies 54 \times (-180) \times 8 = -77760$

$\implies 432 \times (-180) = -77760$

$\implies -77760 = -77760$

Hence Verified !