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Four brothers have ages which are consecutive even integers. If the product of the ages of the two middle brothers is 528, how old is the oldest brother?

**must use algebra**

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5 votes

Answer:

The oldest brother is of age
26 years.

Explanation:

As the age of four brothers are consecutive even integers.

We assume that the ages are
x,(x+2),(x+4),(x+6) as their respective ages.

And the age of the youngest brother
x yrs.

Age of the oldest brother
(x+6) yrs.

According to the question

Product of two middle brother that is
(x+2)(x+4) =528

So we will arrange this in our equation and solve the quadratic.


(x+2)(x+4) =528


x^(2)+4(x)+2(x)+8 =528


x^(2)+4(x)+2(x)+8-528=0


x^(2)+6(x)-520=0

Solving the quadratic by using middle term splitting or directly with quadratic formula we can find the value of 'x' .

Here it is solved with quadratic formula:

Comparing with standard equation
ax^(2)+b(x)+c=0,here
a=1,b=6\ and\ c=-520.


x= (-b \pm √(b^2-4ac) )/(2a) = (-6 \pm √(6^2-4* \ (-520)) )/(2* 1)


x=20,-26

We will work with the positive value of (x) so the the age of the youngest brother
=(x)=20 yrs.

And the age of the the oldest brother
=(x+6)=(20+6)=26 years.

The age difference is of
(26-20)=6 years.

User David Wohlferd
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