One-third of Olivia’s age, increased by 12, is equal to twice her age, decreased by 3. How old is Olivia?
9-years-old.
1/3O + 12 = 2O - 3
9 = 1 2/3 O = 5/3O
Multiply both sides by 3/5.
To solve this problem, we need to translate the given information into an equation.
Let's start by assigning a variable to Olivia's age. Let's say x represents Olivia's age.
According to the problem, one-third of Olivia’s age, increased by 12, is equal to twice her age, decreased by 3.
One-third of her age is (1/3)x. Increasing this by 12 gives us (1/3)x + 12.
Twice her age is 2x. Decreasing this by 3 gives us 2x - 3.
So we can write the equation as:
(1/3)x + 12 = 2x - 3
Now, let's solve the equation to find the value of x:
Multiply both sides of the equation by 3 to eliminate the fraction:
3 * ((1/3)x + 12) = 3 * (2x - 3)
This simplifies to:
x + 36 = 6x - 9
Next, let's gather the x terms on one side of the equation:
x - 6x = -9 - 36
This simplifies to:
-5x = -45
Now, divide both sides of the equation by -5 to solve for x:
x = -45 / -5
This gives us:
x = 9
Therefore, Olivia is 9 years old.