Question

Elizabeth has a lot of jewelry. She has four times as many earrings as watches but half the number of necklaces as earrings. Elizabeth has the same number of necklaces as bracelets. If Elizabeth has 117 pieces of jewelry, has many earrings does she have

Answer 1

Given:
Total number of pieces: 117
watch = x
earrings = four times as many earring as watches = 4x
necklaces = half the number of necklaces as earrings = 1/2 * 4x = 2x
bracelets = necklaces = 2x

x + 4x + 2x + 2x = 117
9x = 117
x = 117/9
x = 13

watches: x = 13
earrings: 4x = 4(13) = 52
necklaces: 2x = 2(13) = 26
bracelets: 2x = 2(13) = 26

13 + 52 + 26 + 26 = 117

There are 13 watches, 52 earrings, 26 necklaces, and 26 bracelets.