Cheryl is fitting a turquoise stone into a bear claw pendant. Find the diameter of the hole in the pendant.
(The diameter, which is 7/8 inches, is the distance across the center of the hole. The two areas outside the hole are 3/16 inches in length.)
To find the diameter of the hole in the pendant, we need to subtract the lengths of the two areas outside the hole from the total length of the pendant.
The total length of the pendant is the sum of the lengths of the two areas outside the hole and the diameter. Given that the two areas outside the hole are 3/16 inches in length each, and the diameter is 7/8 inches, we can set up the equation:
Total length = Length of area 1 + Length of area 2 + Diameter
Let's label the length of area 1 as x and solve for x:
Total length = x + x + Diameter
Since the length of area 1 is x and the length of area 2 is also x, we can rewrite the equation as:
Total length = 2x + Diameter
Substituting the given lengths, we get:
Total length = 2(3/16) + 7/8
Now let's calculate the total length:
Total length = 6/16 + 7/8
To add these fractions, we need to find a common denominator. The least common denominator for 16 and 8 is 16. So, we convert 6/16 to have a denominator of 16:
Total length = 6/16 + 7/8 = 6/16 + 14/16
= 20/16
Now, let's simplify the fraction:
Total length = 20/16 = 10/8 = 5/4
We know that the total length of the pendant is 5/4 inches. To find the diameter, we subtract the sum of the two outside areas (3/16 + 3/16 = 6/16 = 3/8) from the total length:
Diameter = Total length - Length of area 1 - Length of area 2
= 5/4 - 3/8
= 10/8 - 3/8
= 7/8
Therefore, the diameter of the hole in the pendant is 7/8 inches.