It is just a matter of translating the English to Math.
Going with your definitions of A and B
"the sum of their ages" ---> A + B
"the difference of their ages" --> A-B
"is equal to 5 times" ---> = 5(....
(the sum of their ages) is equal to 5 times the difference of their ages
--> A+B = 5(A-B)
or
A+B = 5A - 5B
6B = 4A
B = (2/3)A or 2A/3
Now do the same analysis for the first part of the question.
so back in A^2 - 2B^2 = 6(A-B) = 6A - 6B
A^2 - 2(2A/3)^2 = 6A - 6(2A/3)
A^2 - 8A^2 /9 = 6A - 4A = 2a
times 9 to clear fractions
9A^2 - 8A^2 = 18A
A^2 - 18A = 0
A(A-18) = 0
A = 0 or A = 18 , A=0 clearly does not work
So Ann is 18 and Betty is 12
check:
square of Ann's age = 324
Twice the square of Betty's age = 288
that difference is 36
6 times the difference of their ages = 6(18-12) = 36
both results are 36, so my answer is correct
Ann is older than Betty. Their ages in years are such that twice the square of Betty's age subtracted from the square of Ann's age gives a number equal to 6 times the difference of their ages. Given also that the sum of their ages is equal to 5 times the difference of their ages, find the age in years if each of the sisters.
This question is actually from my exercise book. The answer shows:
Let Ann be A and Betty be B
A^2-2B^2= 6(A-B)
A+B=5(A-B)=
5A-5B
I don't understand the part where they wrote (a+b)=5(a-b), could someone explain it to me. Much appreciated!
2 answers
Thanks
2 answers