Question

The sum of three numbers is 98. The ratio of the first to the second is 2/3 and the ratio of the second to the third is 5/8. What is the second number?

Answer 1

`=>n_2=30`

Explanation:

Let the first number be `n_1`

Let the second number be `n_2`

Let the third number be `n_3`

Given that `(n_1)/(n_2) = 2/3`

Given that `(n_2)/(n_3) = 5/8`

Given that `n_1+n_2+n_3=98` .................................(1)
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Consider `(n_1)/(n_2) = 2/3`

Write this as `3n_1=2n_2`

So `n_1=2/3n_2` .................................................(2)

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Consider `(n_2)/(n_3) = 5/8`

Write this as `8n_2=5n_3`

So `n_3=8/5n_2`......................................................(3)

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

`color(brown)(n_1+n_2+n_3=98color(blue)(" "->" "2/3n_2+n_2+8/5n_2=98`

`=>n_2((10+1+24)/15)=98`

`=>n_2=30`