A painter has painted 1/3 of a rectangular wall that is 12 feet high. When he will paint another 50 square feet of the wall he will have finished 50% of the job. What is the length of the wall?
Let's break down the problem step by step:
The painter has painted 1/3 of a rectangular wall that is 12 feet high. Let's call the length of the wall "L" feet.
When he paints another 50 square feet of the wall, he will have finished 50% of the job.
First, let's find the total area of the wall. The area of a rectangle is given by the formula: Area = Length × Height.
In this case, the height of the wall is given as 12 feet, and we want to find the length (L) of the wall.
So, the total area of the wall is: Total Area = L × 12 square feet.
Next, the painter has already painted 1/3 of the wall, which is (1/3) × Total Area. We can represent this as:
Painted Area = (1/3) × L × 12 square feet.
Now, the painter wants to finish 50% of the job by painting an additional 50 square feet. This means that the Painted Area plus 50 square feet is equal to half of the Total Area:
Painted Area + 50 = (1/2) × Total Area
Substitute the expressions for Painted Area and Total Area:
(1/3) × L × 12 + 50 = (1/2) × L × 12
Now, let's solve for L:
Multiply both sides by 6 to get rid of the fractions:
2L × 12 + 300 = 3L × 12
24L + 300 = 36L
Subtract 24L from both sides:
300 = 12L
Now, divide by 12 to find the length L:
L = 300 / 12 = 25 feet
So, the length of the wall is 25 feet.
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