A pole is painted red, blue and green. One third (1/3) of the pole is painted red and one half (1/2) of the poles
is painted blue. Five feet of the pole is painted green. What is the height of the pole?
(1/3)x + (1/2)x + 5 = x
(5/6)x + 5 = x
5 = (1/6)x
5 / (1/6) = x
5 * 6 = x
30 = x
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Let's assume the height of the pole is "x" feet.
According to the given information, one-third (1/3) of the pole is painted red, which means (1/3)*x feet is painted red.
Also, one-half (1/2) of the pole is painted blue, which means (1/2)*x feet is painted blue.
And, five feet of the pole is painted green.
So, we can write the equation as:
(1/3)*x + (1/2)*x + 5 = x
To solve this equation, we will get rid of the denominators by multiplying the entire equation by 6 (the least common multiple of 3 and 2):
6 * (1/3)*x + 6 * (1/2)*x + 6 * 5 = 6 * x
2x + 3x + 30 = 6x
Combining like terms, we get:
5x + 30 = 6x
Subtracting 5x from both sides, we get:
30 = x
Therefore, the height of the pole is 30 feet.
To find the height of the pole, we need to determine the total length of the pole.
Let's start by calculating the lengths of the red and blue parts of the pole.
Given that one-third (1/3) of the pole is painted red and one-half (1/2) is painted blue, we can represent these fractions as ratios of the total length of the pole.
Let's assume the height of the pole is x feet.
The length of the red part of the pole is 1/3 * x.
The length of the blue part of the pole is 1/2 * x.
Adding these lengths together gives us:
(1/3 * x) + (1/2 * x)
Now, we know that 5 feet of the pole is painted green. So, the remaining length of the pole, which is not painted, is equal to the length of the green part:
Remaining length = x - 5
Now we can set up an equation:
(1/3 * x) + (1/2 * x) = x - 5
To solve for x, we need to simplify the equation. To do that, we can find a common denominator for the fractions:
(2/6 * x) + (3/6 * x) = x - 5
(5/6 * x) = x - 5
Now, multiply both sides of the equation by 6 to eliminate the fraction:
5x = 6(x - 5)
5x = 6x - 30
Subtract 6x from both sides:
5x - 6x = -30
-x = -30
Multiply both sides by -1 to isolate x:
x = 30
Therefore, the height of the pole is 30 feet.