Question

The product of the ages of a father and his son is 576.if the father is 18 years younger than 5 times his son .how old is each?

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Answer 1

`F = 45.4`

`S = 12.68`

Explanation:

Given

Represent the sons age with S and the father's age with F

`S * F = 576`

`F = 5S - 18`

Required

Determine F and S

Substitute 5S - 18 for F in the first equation

`S * (5S - 18) = 576`

Open Bracket

`5S\² - 18S = 576`

Equate to 0

`5S\² - 18S - 576 = 0`

Solve using quadratic formula:

`S = (-b\±√(b^2 - 4ac))/(2a)`

Where

`a = 5`

`b = -18`

`c = -576`

`S = (-b\±√(b^2 - 4ac))/(2a)`

`S = (-(-18)\±√((-18)^2 - 4*5*-576))/(2 * 5)`

`S = (18\±√(324 + 11520))/(10)`

`S = (18\±√(11844))/(10)`

`S = (18\±\108.8)/(10)`

`S = (18+108.8)/(10)` or
`S = (18-108.8)/(10)`

`S = (126.8)/(10)` or
`S = (-90.8)/(10)`

`S = 12.68` or
`S = -9.08`

Since, age can't be negative.

We have that:

`S = 12.68`

Recall that:

`F = 5S - 18`

`F = 5 * 12.68 - 18`

`F = 45.4`

Hence:

The father is 45 years old and the son is 13 years old (Approximated)