Question

The Johnson twins were born two years after their older sister. This year, the product of the three siblings ages is exactly 4558 more than the sum of their ages. How old are the twins?

Answer 1

so we have
johnson twins are x and x since they are same age
the olders subbling is y just because

so 2 years after
x is 2 years after y
y is 2 years older than x
y=2+x


they product (multiply) is 4558 more than sum (add) of ages


so
product of ages=y times x times x
sum=y+x+x

product is 4558 more than sum
y times x times x=4558+y+x+x
what we can do it subsitute y=2+x for y
(2+x) times x tiems x =4558+2+x+x+x
add like terms
(2+x) times x times x=4560+3x
mltipliy
(2+x) times x^2=4560+3x
(2+x) times x^2=(x^2)(2+x)
distribute
2x^2+x^3=4560+3x
subtract 4560+3x from boths ides
x^3+2x^2-3x-4560=0
if we use our trusty TI-89 to factor we get
(x-16.3151)(x^2+17.3151)=0
set each to zero
(x-16.3151)=0
add 16.3151 to both sides
x=16.3151


(x^2+17.3151)=0
subtract 17.3151 from both sides
x^2=-17.3151
impossible except for immaginarry roots


so the answer is the twins are 16.3151 years old or aprox 16 years old

the answer is the twins are 16 years old