Question

the sum of three numbers is 98 the ratio of the following to the second is 2:3 and the ratio of the second to the third is 5 is to8 find the three numbers

Answer 1

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)


Consider n1n2=23

Write this as 3n1=2n2

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



Consider n2n3=58

Write this as 8n2=5n3

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



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

n1+n2+n3=98 → 23n2+n2+85n2=98

⇒n2(10+1+2415)=98

⇒n2=30

Answer 2

Answer:

Step-by-step explanation:

Let the three numbers be x, y and z.

Sum of the numbers is 98.

x + y + z = 98………………(i)

The ratio of the first to the second is 2/3.

x/y = 2/3.

x = 2/3 × y.

x = 2y/3.

The ratio of the second to the third is 5/8.

y/z = 5/8.

z/y = 8/5.

z = 8/5 × y.

z = 8y/5.

Put the value of x = 2y/3 and z = 8y/5 in (i).

2y/3 + y + 8y/5 = 98

49y/15 = 98.

49y = 98 × 15.

49y = 1470.

y = 1470/49.

y = 30 .

Therefore, the second number is 30.