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Mrs. Arithmetic and Mrs. Algebra (Posted on 2022-07-05)

When asked about the ages of her three children, Mrs. Arithmetic replied to Mrs. Algebra in the following manner:

"The sum of the ages of my children is precisely 3 times that of Alec who is 3 years younger than Laura. The cube of Laura's age together with the square of Alec's age plus Karl's age make up a multiple of 100"

Determine the ages of the three children if Alec is still in his twenties.

No Solution Yet Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Possible Solution

| Comment 3 of 4 |

Since l=(a+3), for the sum of ages we have (a+k+(a+3)=3a, so k=(a-3)

Now we have (a+3)^3+a^2+(a-3)= (a+2)^2(a+6) as a number divisible by 100.

But looking at the square term, we have (a+2)^2=900 if a=28.

Trying 28: (28+2)^2(28+6) = 30600

Since Ales is 28, Laura is 31 and Karl is 25.

Edited on July 5, 2022, 9:41 pm

Posted by broll on 2022-07-05 21:39:55

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