Anyone, please help:
The figure below, not drawn to scale is made up of a square, a rectangle and a triangle, 1/6 of the square is shaded, 1/5 of the triangle is shaded and 1/4 of the rectangle is shaded. IF THE SHADED AREA IS 7/17 of the shaded area of the triangle, what fraction of the total area of the figure is not shaded?
apparently the sum of all the shaded areas is less than the shaded area of the triangle. I don't see how that can be.
41%
To find the fraction of the total area of the figure that is not shaded, we need to determine the fraction of the total area that is shaded first.
Let's assume the total area of the figure is represented by the fraction 1.
Given the information:
- 1/6 of the square is shaded
- 1/5 of the triangle is shaded
- 1/4 of the rectangle is shaded
Let's represent the shaded area of the square as x, the shaded area of the triangle as y, and the shaded area of the rectangle as z.
Since the shaded area is 7/17 of the shaded area of the triangle, we can set up the following equation:
(x + y + z) / y = 7/17
Now, let's find the fractions of the shaded areas:
1/6 of the square is shaded, so x = 1/6.
1/5 of the triangle is shaded, so y = 1/5.
1/4 of the rectangle is shaded, so z = 1/4.
Substituting the values into the equation:
(1/6 + 1/5 + 1/4) / (1/5) = 7/17
To simplify the equation, we need to find a common denominator:
(20/120 + 24/120 + 30/120) / (24/120) = 7/17
Combining the fractions in the numerator:
(74/120) / (24/120) = 7/17
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(74/120) × (120/24) = 7/17
Simplifying the equation:
3115/2880 = 7/17
Now, let's find the fraction of the total area that is not shaded:
The total area of the figure is represented by the fraction 1.
The fraction of the shaded area is 7/17.
To find the fraction of the total area that is not shaded, we subtract the fraction of the shaded area from 1:
1 - 7/17 = (17/17 - 7/17) = 10/17.
Therefore, the fraction of the total area of the figure that is not shaded is 10/17.
To solve this problem, we need to find the fraction of the total area of the figure that is not shaded.
Let's break down the problem step by step:
Step 1: Determine the fraction of the shaded area of the triangle: Since the problem states that the shaded area is 7/17 of the shaded area of the triangle, we can represent this as:
Fraction of shaded area of triangle = 7/17
Step 2: Find the fraction of the shaded area of the square: The problem states that 1/6 of the square is shaded. Therefore, the fraction of the shaded area of the square is:
Fraction of shaded area of square = 1/6
Step 3: Find the fraction of the shaded area of the rectangle: The problem states that 1/4 of the rectangle is shaded. Therefore, the fraction of the shaded area of the rectangle is:
Fraction of shaded area of rectangle = 1/4
Step 4: Calculate the total shaded area: To find the total shaded area, we add the fractions of the shaded areas of the triangle, square, and rectangle:
Total shaded area = Fraction of shaded area of triangle + Fraction of shaded area of square + Fraction of shaded area of rectangle
Total shaded area = 7/17 + 1/6 + 1/4
Step 5: Subtract the total shaded area from 1 to find the fraction of the total area that is not shaded:
Fraction of not shaded area = 1 - Total shaded area
Now, you can substitute the values and calculate the final fraction.