perplexus.info :: Numbers : Mrs. Arithmetic and Mrs. Algebra

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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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solution

| Comment 2 of 6 |

Alex is 28, Karl is 25, Laura is 31

A, L, K

A + L + K = 3A

A + 3 = L

A = L-3

L^3 + A^2 + K = 100n

A = L-3 **********

K = 2A - L

K = 2(L-3) - L

K = L-6 **********

Let A = a

So (K,A,L) = (a-3,a,a+3)

(a+3)^3 + a^2 + (a-3) = 100n

a^3 + 10a^2 + 28a + 24 = 100n

Since Alex = a and is in his twenties just check 20 <= a < 30

--------------------------

def age_function(a):

return a**3 + 10*a**2 + 28*a + 24

for a in range(20,30):

if age_function(a)%100 == 0:

print(a,age_function(a))

OUTPUT: 28 30600

So Alex is 28, Karl is 25, Laura is 31

Posted by Larry on 2022-07-05 19:05:59

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