the price of a watch, locket and a chain is $216, the price of a watch and a locket is 3 times the price of a chain, the price of a chain and a locket is half of a watch, find the price of the watch, locket and chain
Answers
Watch(W), Chain(C), Locket(L)
W+L=3C(1), C+L=0.5W(2), W+L+C=216(3)
(1)-(2)*2:
W+L-W=3C-C-L
L=2C-L
2L=2C (4) => the locket costs as much as the watch.
=> From (4), 0.5W=2L
W=4L
=> 4L+L+L=216
6L=216
=> L=36, locket costs 36
=> C=L=36, chain costs 36
=> W=4L=144, watch costs 144
Given: Price of watch, locket and chain = $216
Price of watch and locket = 3 times the price of chain
Price of chain and locket = 1/2* price of watch
To find: Price of watch, locket and chain
Let: Price of watch = $X, price of locket = $Y and price of chain = $Z
Solution: According to the given question,
Price of watch + price of locket + price of chain = $216
i.e., X + Y + Z = $216 ...(1)
also, Price of watch and locket = 3 x price of chain
⇒ X + Y = 3 x Z ...(2)
and Price of chain and locket = 1/2 x price of watch
⇒ Y + Z = 1/2 x X ...(3)
Putting value of X + Y from equation (2) in equation (1)
⇒ (3 x Z) + Z = 216
⇒ 3Z + Z = 216
⇒ 4Z = 216
⇒ Z = 54 (Price of chain)
Putting value of Y in equation 2
⇒ X + Y = 3 x (54)
⇒ X + Y = 162
Y = 162 - X and also from equation (3), Y = X/2 - Z
Comparing both the values of Y
⇒ 162 - X = X/2 - Z
⇒ 162 - X = X/2 - 54 (Z = 54)
⇒ 162 + 54 = X/2 + X
⇒ 3X/2 = 216
⇒ 3X = 432
⇒ X = 144
Putting value of X in Y = 162 - X
⇒ Y = 162 - 144 = 18
Hence, the price of watch (X) = $144
Price of locket (Y) = $ 18 and Price of chain (Z) = $54