An oil painting is 16 years older than a watercolor by the same artist. The oil painting is also three times older than the watercolor. How old is each? Identify a variable, set up an equation and solve.
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O = W + 16 = 3W
Solve for W, then either W+16 or 3W.
Let's assume the age of the watercolor painting is x years.
According to the problem, the oil painting is 16 years older than the watercolor. This means the age of the oil painting can be represented as x + 16 years.
The problem also states that the oil painting is three times older than the watercolor. So, we can write the equation as:
x + 16 = 3x
To solve this equation for x, we can subtract x from both sides:
16 = 2x
Next, we can divide both sides of the equation by 2:
x = 8
Therefore, the age of the watercolor painting is 8 years. To find the age of the oil painting, we substitute the value of x back into the equation:
x + 16 = 8 + 16 = 24
So, the age of the oil painting is 24 years.
To solve this problem, we can assign variables to the ages of the oil painting and the watercolor. Let's say the age of the watercolor is x years.
According to the given information, the oil painting is 16 years older than the watercolor, so we can express the age of the oil painting as x + 16 years.
Also, it is stated that the oil painting is three times older than the watercolor. Therefore, we can write the equation as:
x + 16 = 3x
Now, we can solve this equation to find the value of x.
Moving the x from the right side to the left side, we have:
16 = 3x - x
Combining like terms, we get:
16 = 2x
To isolate x, we divide both sides of the equation by 2:
16/2 = x
Simplifying, we find:
8 = x
So, the watercolor is 8 years old.
To find the age of the oil painting, we substitute the value of x into either equation. Using the first equation we set up earlier:
Age of the oil painting = x + 16
Age of the oil painting = 8 + 16
Age of the oil painting = 24
Therefore, the watercolor is 8 years old and the oil painting is 24 years old.