Question

1. In a certain system of gears, the ratio of the number of teeth on the first gear to the number of teeth on the second gear is 7:3. If the first gear has 259 teeth, how many teeth does the second gear have? 2. A circle with diameter 250 cm has circumference 785 cm. How large is the diameter of a circle with circumference 15.7 cm?

Answer 1

Answer: 5

Explanation:

Answer 2

1. 111 teeth on the second gear.

2. Diameter = 5.0 cm

Explanation:

1. The ratio is (7 teeth first gear)/(3 teeth second gear)

We can invert this to (3 teeth second gear)/(7 teeth first gear)

Now multiply by the teeth on the first gear:

[(3 teeth second gear)/(7 teeth first gear)]*(259 teeth first gear)

(3*259)/7 teeth second gear

111 teeth on the second gear.

2. Circumference = 2πr

Circle A: 2(π)(125cm)

Circumference = 285.4 cm

Circle B: 15.7 cm = 2(π)(r)

r = (15.7cm)/(2π)

r = 2.5 cm

Diameter = 5.0 cm