Answer:
[tex]F = 45.4[/tex]
[tex]S = 12.68[/tex]
Step-by-step explanation:
Given
Represent the sons age with S and the father's age with F
[tex]S * F = 576[/tex]
[tex]F = 5S - 18[/tex]
Required
Determine F and S
Substitute 5S - 18 for F in the first equation
[tex]S * (5S - 18) = 576[/tex]
Open Bracket
[tex]5S\² - 18S = 576[/tex]
Equate to 0
[tex]5S\² - 18S - 576 = 0[/tex]
Solve using quadratic formula:
[tex]S = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = 5[/tex]
[tex]b = -18[/tex]
[tex]c = -576[/tex]
[tex]S = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]S = \frac{-(-18)\±\sqrt{(-18)^2 - 4*5*-576}}{2 * 5}[/tex]
[tex]S = \frac{18\±\sqrt{324 + 11520}}{10}[/tex]
[tex]S = \frac{18\±\sqrt{11844}}{10}[/tex]
[tex]S = \frac{18\±\108.8}{10}[/tex]
[tex]S = \frac{18+108.8}{10}[/tex] or [tex]S = \frac{18-108.8}{10}[/tex]
[tex]S = \frac{126.8}{10}[/tex] or [tex]S = \frac{-90.8}{10}[/tex]
[tex]S = 12.68[/tex] or [tex]S = -9.08[/tex]
Since, age can't be negative.
We have that:
[tex]S = 12.68[/tex]
Recall that:
[tex]F = 5S - 18[/tex]
[tex]F = 5 * 12.68 - 18[/tex]
[tex]F = 45.4[/tex]
Hence:
The father is 45 years old and the son is 13 years old (Approximated)
