One-third of Olivia’s age, increased by 12, is equal to twice her age, decreased by 3. How old is Olivia?

Just translate the sentence into Math:

let Olivia's age be x

One-third of Olivia’s age, increased by 12:
(1/3)x + 12
is equal to : =

twice her age, decreased by 3:
2x - 3

put it together, then solve:
(1/3)x + 12 = 3x - 3

I suggest multiplying each term by 3 to get rid of the fraction

25

Let's assume Olivia's age is x.

According to the given information:
One-third of Olivia's age, increased by 12, is equal to twice her age, decreased by 3.

So, we can set up the equation:

(1/3)x + 12 = 2x - 3

First, let's simplify the equation by multiplying each term by the common denominator of 3:

3 * [(1/3)x + 12] = 3 * (2x - 3)
x + 36 = 6x - 9

Next, let's isolate the x term by subtracting x from both sides:

x - x + 36 = 6x - 9 - x
36 = 5x - 9

Now, let's isolate the 5x term by adding 9 to both sides:
36 + 9 = 5x - 9 + 9
45 = 5x

Finally, divide both sides by 5 to solve for x:
45/5 = 5x/5
9 = x

Therefore, Olivia is 9 years old.

To solve this problem, let's break it down step by step:

Let's assume the age of Olivia is "x" years.

According to the problem, the first part states "One-third of Olivia’s age, increased by 12." This can be represented as (1/3)x + 12.

The second part states "is equal to twice her age, decreased by 3." This can be represented as 2x - 3.

The equation can be formed as:

(1/3)x + 12 = 2x - 3

Now, let's solve for x:

First, we can eliminate the fractions by multiplying the entire equation by 3:

x + 36 = 6x - 9

Next, let's get all the "x" terms on one side of the equation by subtracting "x" from both sides:

36 = 5x - 9

Now, let's isolate the "x" term by adding 9 to both sides:

45 = 5x

Finally, divide both sides by 5 to solve for x:

x = 9

Therefore, Olivia is 9 years old.