if the sum of the diameters of two circles is 28 inches one circle has a diameter that is 8 inches longer than the diameter of the other what are the diameters of the two circles
x + x + 8 = 28
2x = 20
x = 10
x = diameter of the smaller circle
x = diameter of 1 circle
x + 8 = diameter of 2nd circle
x + x + 8 = 28
2x + 8 = 28
Solve for x
To find the diameters of the two circles, we can solve this problem using algebraic equations.
Let's assign variables to represent the diameters of the circles. Let the diameter of one circle be x inches. Since the other circle has a diameter that is 8 inches longer, its diameter can be represented as (x + 8) inches.
According to the given information, the sum of the diameters of the two circles is 28 inches. So we can write the following equation:
x + (x + 8) = 28
Simplifying the equation, we have:
2x + 8 = 28
Now, let's isolate the variable:
2x = 28 - 8
2x = 20
Divide both sides of the equation by 2:
x = 20/2
x = 10
Therefore, the diameter of one circle is 10 inches. Substituting this value into the equation (x + 8), we can find the diameter of the other circle:
10 + 8 = 18
Hence, the diameters of the two circles are 10 inches and 18 inches.