77.4k views
3 votes
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?



User Arthurfnsc
by
8.3k points

1 Answer

3 votes

Answer:


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)

User Muhammad Shah
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.