Question

Nine years ago, Katie was twice as old as Elena was then. Elena realizes, "In four years, I'll be as old as Katie is now!" Elena writes these equations to help make sense of the situation: k - 9 = 2(e - 9)

e + 4 = k

If Elena is currently e years old and Katie is k years old, how old is Katie now?

Answer 1

Katie is 17 now

Explanation:

You want to know Katie's current age (k) if the equations relating Katie's and Elena's ages are ...

• k -9 = 2(e -9)
• e +4 = k

Solution

Rewriting the second equation as ...

e = k -4

we can substitute into the first to get ...

k -9 = 2((k -4) -9)

k -9 = 2(k -13)

k -9 = 2k -26

k = 17 . . . . . . . add 26-k to both sides

Katie is 17 years old now.

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Additional comment

Elena is 13 now.

When you learn the difference in ages is 4 years, you know that their ages when Katie was twice as old were 4 and 8 (the difference is equal to Elena's age then). Since that was 9 years ago, their current ages are ...

Elena is 13, Katie is 17.

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