SOLUTION: sofia is 12 years older than her sister anna - maria. the product of their age is 540, how old is sofia

Question 555745: sofia is 12 years older than her sister anna - maria. the product of their age is 540, how old is sofia
Answer by TutorDelphia(193) (Show Source): You can put this solution on YOUR website!
sofia is 12 years older than her sister anna - maria
s=a+12
the product of their age is 540,
s*a=540
Solve for s by dividing both sides by a
s=540/a
sub in 540/a in for s
540/a=a+12
multiply both sides by a to get a off the denominator
540=a^2+12a
subtract 540 from both sides
a^2+12a-540=0
factor the quadratic, list 540's factors or use the quadratic formula
1,540
2,270
3,180
4,135
5,108
6,90
9,60
10,54
12,45
18,30
20,27

18 and 30 are the only ones that have a difference of 12.
(a- 18)(a+ 30)=0
a-18=0
a=18
a+30=0
a=-30
s=18+12
s=30
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