Question 584732
Let j = Jenna's age
Let s = Sarah's age
:
Write an equation for each statement:
:
"Sarah' age is twice as jJenna's."
s = 2j
:
"Jennas present age is two more than twice the quotient of Sarah's and Jenna's ages four years ago."
j = 2({{{(s-4)/(j-4)}}}) + 2
subtract 2 from both sides
j - 2 = 2({{{(s-4)/(j-4)}}})
Divide both sides by 2
{{{(j-2)/2}}} = {{{(s-4)/(j-4)}}} 
Cross multiply
(j-2)(j-4) = 2(s-4)
FOIL the left side
j^2 - 4j - 2j + 8 = 2s - 8
j^2 - 6j + 8 = 2s - 8
Replace s with 2j
j^2 - 6j + 8 = 2(2j) - 8
j^2 - 6j + 8 = 4j - 8
Combine like terms on the left
j^2 - 6j - 4j + 8 + 8 = 0
j^2 - 10j + 16 = 0
Factors to
(j-2)(j-8) = 0
Two solutions
j = 2, not possible, since they talk about 4 yrs ago
and
j = 8, a good solution
:
How old are Sarah and Jenna now.
If j = 8, then s = 16
:
You can check the solutions in the original statement
"Jennas present age is two more than twice the quotient of Sarah's and Jenna's ages four years ago."
8 = 2({{{(16-4)/(8-4)}}}) + 2