Question 1196117: the product of the age of mona and her mother is 546. if her mother is 10 lessb than thrice her age. how old is mona and her mother? Found 2 solutions by josgarithmetic, greenestamps:Answer by josgarithmetic(39617) (Show Source):
For a quick, informal solution, simply look for two numbers whose product is 546 that satisfy the condition that the larger is 10 less than 3 times the smaller.
546=6*91=2*3*7*13
Two combinations look promising: 13 and 42, or 14 and 39. See which one (if either) works.
3(13)-10 = 39-10 = 29 (not 42); that doesn't work
3(14)-10 = 42-10 = 32 (not 39); that doesn't work either
No other combination works either.
Since age problems must have solutions that are whole numbers, the problem is defective.
Check to see if you have stated the problem correctly; if not, re-post with the correct information.
Note if the given information were correct, the setup for an algebraic solution would be easy:
x = Mona's age
3x-10 = mother's age
x(3x-10)=546
3x^2-10x=546
3x^2-10x-546=0
But that quadratic does not factor over the integers....
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