Question

the sum of 4 numbers is 771. the ratio of the first to second number is 2:3. the ratio of the second to third is 5:4. the ratio of the third to the fourth is 5:6. find the value of the second number

Answer 1

Answer:

The second number is 225.

Step-by-step explanation:

Consider the provided information.

Let the first number is x.

Second number

$\dfrac{x}{\text{Second number}} =\dfrac{2}{3}\\\\\text{Second number}=\dfrac{3}{2}x$

Third number is:

$\dfrac{\text{Second number}}{\text{Third number}} =\dfrac{5}{4}\\\\\text{Third number}=\dfrac{3}{2}x\times\dfrac{4}{5}=\dfrac{6}{5}x$

Fourth number is:

$\dfrac{\text{Third number}}{\text{Fourth number}} =\dfrac{5}{6}\\\\\text{Fourth number}=\dfrac{6}{5}x\times\dfrac{6}{5}=\dfrac{36}{25}x$

The sum of 4 numbers is 771.

$x+\dfrac{3}{2}x+\dfrac{6}{5}x+\dfrac{36}{25}x=771$

$50x+75x+60x+72x=38550$

$257x=38550\\x=150$

First number is 150.

$\text{Second number}=\dfrac{3}{2}\times150=225$

Hence, the second number is 225.