Any clever Mathematician, be able to help solve this for me?
Babara visited her High School friend, Natasha after their 25th school reunion. “What a nice pair of children you have, are they twins?, Babara asked.
“No my sister is older I,” said Natasha’s son Philip. “The square of my age plus the cube of her age is 7148.”
“The square of my age plus the cube of his age is 5274,” said Matilda.
How old are they?
Philip = ? y.o. Matilda = ? y.o.
Favorite Answer
y^2+x^3=5274
This would be difficult to solve directly, so You use the info given above to guess.
Facts:
1) ages are integers
2) the two are a few years (1 or 2) apart.
3) They are teenagers, since it’s a 25 year high school reunion.
So we guess, their ages must be 17, 18, 19 or 204
Start with 19.
19*19*19 = 6859
7148 – 6859 = 289 = 17*17
so their ages are 17 and 19 !!!
17*17*17 = 4913 19*19 = 361 4913 + 361 = 5274 checks!
solving the system you just mentioned:
p2 + m3 – m2-p3=7148 – 5274 = 1874
(m-p)(m2-mp+p2-m-p) = 2 * 937
lets say : m-p = 2
m= p+2
plug this into second equation and solve it out ; you will get the results.
Take Matilda’s age to be M.
M^3+P^2=7148
M^2+P^3=5274
solve system.
