SOLUTION: how whould i set up an equation for this word problem four years ago, katie was twice as old as anne was then. in 6 years, anne will be the same age that katie is now. how old is

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Question 133068This question is from textbook
: how whould i set up an equation for this word problem
four years ago, katie was twice as old as anne was then. in 6 years, anne will be the same age that katie is now. how old is each now? This question is from textbook

Answer by solver91311(24713) About Me  (Show Source):
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Katie's age now: k
Anne's age now: a

Katie's age 4 years ago: k - 4
Anne's age 4 years ago: a - 4

Anne's age 6 years from now: a + 6

Four years ago, katie was twice as old as Anne was then: k-4=2%28a-4%29
In 6 years Anne will be the same age as Katie is now: k=a%2B6

k-4=2%28a-4%29
k-4=2a-8
k-2a=-4

Since we know that k=a%2B6, we can substitute:
cartoon%28red%28k%29-2a=-4%2Cred%28%28a%2B6%29%29-2a=-4%29

Collect like terms:
a-2a=-4-6
-a=-10

Multiply both sides by -1:
a=10, and k=a%2B6=10%2B6=16

So Katie is 16 and Anne is 10.

Check:
Four years ago, katie was twice as old as Anne was then:

16 - 4 = 12
2 * (10 - 4) = 2 * 6 = 12

In 6 years Anne will be the same age as Katie is now:

10 + 6 = 16

Answer checks.