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?

1 Answer
Jul 26, 2016

=>n_2=30n2=30

Explanation:

Let the first number be n_1 n1

Let the second number be n_2 n2

Let the third number be n_3 n3

Given that (n_1)/(n_2) = 2/3n1n2=23

Given that (n_2)/(n_3) = 5/8n2n3=58

Given that n_1+n_2+n_3=98n1+n2+n3=98 .................................(1)
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Consider (n_1)/(n_2) = 2/3n1n2=23

Write this as 3n_1=2n_23n1=2n2

So n_1=2/3n_2n1=23n2 .................................................(2)

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Consider (n_2)/(n_3) = 5/8n2n3=58

Write this as 8n_2=5n_38n2=5n3

So n_3=8/5n_2n3=85n2......................................................(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=98n1+n2+n3=98 23n2+n2+85n2=98

=>n_2((10+1+24)/15)=98n2(10+1+2415)=98

=>n_2=30n2=30