Question

The sum of three numbers is $\mathfrak\purple{98}$. The ratio of the first to the second is $\mathfrak\red{\dfrac{2}{3}}$, and the ratio of the second to the third is $\mathfrak\green{\dfrac{5}{8}}$. Find the second number ​

Answer 1

Answer:

Let the first number be n1

Let the second number be n2

Let the third number be n3

Given that n1n2=23

Given that n2n3=58

Given that n1+n2+n3=98.................................(1)

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Consider n1n2=23

Write this as 3n1=2n2

So n1=23n2 .................................................(2)

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Consider n2n3=58

Write this as 8n2=5n3

So n3=85n2......................................................(3)

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Substitute (3) and (2) into (1) giving:

n1+n2+n3=98 → 23n2+n

Answer 2

Let the three parts be A, B, C. Then,

A : B = 2 : 3 and B : C = 5 : 8

$b = (5 \times \frac{3}{5} ) \: : \: (8 \times \frac{3}{5} ) = 5 \: : \frac{24}{5}$

$a \: : \: b \: : \: c = 2 \: : \: 3 \: : \: \frac{24}{5} = 10 \: : \: 15 \: : \: 24$

The second number B is

$b = (98 \times \frac{15}{49} )$

B = 30

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