##### mathcounts problem 26

label Mathematics
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Currently, the sum of the ages of Yumi, Rana and Victoria is 42 years. Four years ago, the sum of the ages of Rana and Victoria was equal to the current age of Yumi. What is Yumi's current age?

Oct 20th, 2017

let Yumi's age be =x, Rana's age be y and Victoria's age be z

so the sum of age currently should be x+y+z = 40

also given is 4 years ago,

so 4 years ago, age of Yumi was = (x-4) year old
Rana was = (y-4) year old
Victoria was = (z-4) year old

the sum of the ages of Rana and Victoria was equal to the current age of Yumi.

so, current age of yumi =  four years ago the sum of the ages of Rana and Victoria
i.e. X = (y-4)+(z-4)
or, x = y+z-4-4

since, x+y+z=40 as derived earlier, so y+z = 40-x
putting the value of y+z in the above equation,
x=40-x-8
or, 2x = 32
or, X =32/2 = 16

so Yumi's Current age is 16 years old.

Please best my answer if it was helpful to you. I have tried to explain in as much detail as possible :)

Dec 26th, 2014

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Oct 20th, 2017
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Oct 20th, 2017
Oct 21st, 2017
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