The radii of the two concentric circles are 3: 7. Find the diameters of these circles if the width

The radii of the two concentric circles are 3: 7. Find the diameters of these circles if the width of the ring formed by them is 24 cm.

Let us denote the radius of the smaller circle by the letter r, and the larger one by R.
According to the conditions of the problem, r / R = 3/7.
The width of the strip will be equal to R-r and, according to the conditions, is equal to 24 (cm), which means: R-r = 24 (cm), that is, R = r + 24 (cm).
Taking into account the obtained result, we have:
r / r + 24 = 3/7,
7r = 3 * (r + 24),
7r = 3r + 72,
4r = 72,
r = 18 (cm).
Since R = r + 24, then R = 18 + 24 = 42 (cm).
Thus, the diameter of one circle will be equal to D = 2R = 42 * 2 + 84 (cm), and the diameter of the second circle will be equal
d = 2r = 18 * 2 = 36 (cm).

Answer. 36 cm vs 84 cm.