Answer:
Sarah is 13 years old
Step-by-step explanation:
Represent Sarah's age with S
Her first brother's age with F
Her second brother's age with B
So, we have:
From the first statement, we have:
[tex]S - F = 5[/tex] ---- (1)
From the second, we have:
[tex]S - B = 8[/tex] ---- (2)
The product of their ages is 40.
First, we make F the subject in (1) and B the subject in (2)
[tex]F = S - 5[/tex]
[tex]B = S - 8[/tex]
Their product is represented as follows:
[tex]F * B = 40[/tex]
Substitute values for F and B
[tex](S - 5) * (S - 8)=40[/tex]
Open bracket
[tex]S^2 - 5S -8S + 40 = 40[/tex]
[tex]S^2 - 13S + 40 = 40[/tex]
Subtract 40 from both sides
[tex]S^2 - 13S = 0[/tex]
Factorize:
[tex]S(S - 13) = 0[/tex]
Split:
[tex]S = 0[/tex] or [tex]S - 13 = 0[/tex]
But Sarah's age can't be 0 because she has two younger brothers.
So, we stick to
[tex]S - 13 = 0[/tex]
Make S the subject
[tex]S = 13[/tex]
Hence, Sarah is 13 years old
