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The sum of three numbers is 212 .If the ratio of the first to the second is 13:16 and that of the second to the third is 2:3 then find the numbers.`​

User ChanChow
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Given:

The sum of three numbers is 212 .

The ratio of the first to the second is 13:16 and that of the second to the third is 2:3.

To find:

The unknown numbers.

Solution:

We have,

First : Second = 13:16

Second: Third = 2:3

We need to combine these ratios, to get a single ratio for all three numbers.

Second: Third = 2×8:3×8 = 16:24

Now,

First: Second: Third = 13:16:24

Let the first, second and third numbers are 13x, 16x and 24x respectively.


13x+16x+24x=212


53x=212


x=(212)/(53)


x=4

So, the numbers are,


First=13x


First=13(4)


First=52

Similarly,


Second=16x


Second=16(4)


Second=64

And,


Third=24x


Third=24(4)


Third=96

Therefore, the three unknown numbers are 52, 64, 96.

User Korrawit
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