SOLUTION: Sarah' age is twice as jJenna's.Jennas present age is two more than twice the quotient of Sarah's and Jenna's ages four years ago.How old are Sarah and Jenna now.
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Question 584732: Sarah' age is twice as jJenna's.Jennas present age is two more than twice the quotient of Sarah's and Jenna's ages four years ago.How old are Sarah and Jenna now.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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() + 2
subtract 2 from both sides
j - 2 = 2()
Divide both sides by 2
=
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() + 2
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