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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.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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computer-aided solution

| Comment 1 of 6

clc

for laura = 4:150

alec=laura-3;

% alec+laura+karl=3*alec

karl=2*alec-laura;

testSum=laura^3+alec^2+karl;

if testSum/100==round(testSum/100)

disp([alec laura karl testSum])

end

finds

         Alec       Laura        Karl   L^3+A^2+K
           8          11           5        1400
          18          21          15        9600
          28          31          25       30600
          38          41          35       70400
          44          47          41      105800
          48          51          45      135000
          58          61          55      230400
          68          71          65      362600
          78          81          75      537600
          88          91          85      761400
          94          97          91      921600
          98         101          95     1040000
         108         111         105     1379400
         118         121         115     1785600
         128         131         125     2264600
         138         141         135     2822400
         144         147         141     3197400

of which only

Alec = 28, Laura = 31, Karl = 25 satisfies Alec being in his twenties.

Posted by Charlie on 2022-07-05 13:11:05

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