Question

The sum of three numbers is 98. If the ratio of the first to second is 2:3 and that of the second to the third is 5:8; then the second number is

Answer 1

⇒n2=30

Step-by-step explanation:

⇒n2=30

Step-by-step explanation:

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+n2+85n2=98

⇒n2(10+1+2415)=98

⇒n2=30

Answer 2

30

Step-by-step explanation:

Since the ratio between the first/ second number is 2 : 3

Let them be represented by

2x : 3x

The ratio between the second/ third numbers is 5 : 8, then

third number =
`(8)/(5)` × 3x =
`(24)/(5)` x = 4.8x

We have the 3 numbers in the ratio 2x : 3x : 4.8x

Sum the numbers and equate to 98

2x + 3x + 4.8x = 98

9.8x = 98 ( divide both sides by 9.8 )

x = 10

Hence the 3 numbers are

2x = 20, 3x = 30 and 4.8x = 48, that is

20, 30, 48 ← sum = 98

Thus the second number is 30