Sylvia has a jewelry collection of bracelets, necklaces, and earrings. She has 16 bracelets. The number of earrings is 2 times the number of necklaces. She has 43 pieces of jewelry in all. How many of each piece of jewelry does she have?
Let x = the number of necklaces.
16 + 2x + x = 43
16 + 3x = 43
3x = 43 - 16
3x = 27
x = 27/3
x = ?
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To solve this problem, let's assign variables to the unknown quantities:
Let's say the number of necklaces Sylvia has is 'N'.
Then, the number of earrings she has is '2N' (since it is stated that the number of earrings is 2 times the number of necklaces).
We already know that Sylvia has 16 bracelets. Let's assign that as 'B'.
According to the problem, Sylvia has a total of 43 pieces of jewelry. So the equation can be formed as:
B + N + 2N = 43
Simplifying the equation:
B + 3N = 43
Now we can substitute the value of B (16) into the equation:
16 + 3N = 43
Next, we need to isolate the variable N by subtracting 16 from both sides:
3N = 43 - 16
3N = 27
Finally, we can solve for N by dividing both sides by 3:
N = 27 / 3
N = 9
So, Sylvia has 9 necklaces. Since the number of earrings is 2 times the number of necklaces, Sylvia must have:
2N = 2 * 9
2N = 18 earrings
Therefore, Sylvia has 16 bracelets, 9 necklaces, and 18 earrings.