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The sum of Ivy's and Audrey's ages is 27. Nine years ago, Ivy was

twice as old as Audrey. How old is each now?

User Com
by
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1 Answer

2 votes

Answer:

Ivy is 15 years old and Audrey is 12 years old.

Explanation:

Let Ivy's age be
i and Audrey's age be
a.

Since the sum of their ages is 27, we can write the equation
i+a=27.

Next, we'll write a second equation from the fact that 9 years ago Ivy was twice as old as Audrey. Nine years ago, Ivy and Audrey's ages were
i-9 and
a-9, respectively. Therefore, we have
i-9=2(a-9)

Let's isolate
i by adding 9 to both sides:


i=2(a-9)+9

Distribute:


i=2a-18+9,\\i=2a-9

Now substitute
i=2a-9 into our first equation:


2a-9+a=27,\\3a-9=27, \\3a=36, \\a=\boxed{12}

Therefore, Ivy's age must be:


i+12=27,\\i=27-12=\boxed{15}

Thus, Ivy must be 15 years old and Audrey must be 12 years old.

User ArleyM
by
6.6k points