Megan is half her mother's age. next year both megan's age and her mother's age will be a perfect square. how old is megan's mother this year?

Y u use same letter name
ok, we wil cal them kid and mom
k=kid's age
m=mom's age

kid is half mom's age
k=1/2m

next year (both ages increased by 1)
megan's age and mom's age will be perfect square
k+1=r²
m+1=c²
where c and r are whole numbers

ok, one way is to list all the perfect squares, decrease them by 1 and find which ones are double of another perfec tsquare

0,1,4,9,16,25,36,49,64,81,100
decrease by 1
-1,0,3,8,15,24,35,48,63,80,99
ah, 24 and 48

their ages are 24 and 48