A in isolation art gourmet sole the board during the 10% detriment during the monetary depression. She paid for it years after during an auction as well as sole it to the notable relic for $37,000 some-more than the auction price.
If the art studio done the 25% distinction as well as the gourmet done the 39.5% net distinction upon her strange investment, for what cost did she creatively paid for the picture.
{ 2 comments… read them below or add one }
Let:
Op = original price
Fp = financial depression price
Ap = auction price
Sp = price as sold to museum
Eqn1:
Fp = 0.90(Op); A private art collector sold a canvas at a 10% loss during a financial depression
Eqn2:
Sp = Ap + 37,000; She bought it years later at an auction and sold it to a museum for $37,000 more than the auction price.
Eqn3:
(Ap – Fp) / Fp = 0.25; the gallery made a 25% profit
Eqn4:
(Sp – Op)/Op = 0.395; the collector made a 39.5% net profit on her original investment
Find: Op
Solution:
From Eqn3:
(Ap – Fp) / Fp = 0.25
Ap – Fp = 0.25Fp
Ap = Fp + 0.25Fp
Ap = 1.25Fp Eqn5
SubstituteEqn1 to Eqn5:
Ap = 1.25Fp
Ap = 1.25(0.90Op)
Ap = 1.125Op Eqn6
From Eqn4:
(Sp – Op)/Op = 0.395
Sp – Op = 0.395Op
Sp = Op + 0.395Op
Sp = 1.395Op Eqn7
Substitute Eqn6 and Eqn7 to Eqn2, then solve for Op:
Sp = Ap + 37,000
1.395Op = Ap = 1.125Op + 37,000
1.395Op – 1.125Op = 37,000
0.27Op = 37,000
Op = 37,000/0.27
Op = 137,037
Therefore, the collector’s original investment was $137,037.
The progress of the equation will be shown in ()
Expenditures will be negative, and profit will be positive
We’ll set p= original price (-p = )
The 39.5% net profit gives us an answer, which is 1.395p (it’s not just .395 because it has to be more) (-p = 1.395p)
Which makes .9p = selling price (-p + .9p = 1.395p)
Since the gallery made a 25% profit, that’s 1.25 * .9p = 1.125p how much she bought it for (-p + .9p -1.125p = 1.395p)
She then sells it for 37000 more, finishing the equation: -p + .9p – 1.125p + 1.125p + 37000 = 1.395p
Combine like terms on each side: -.1p + 37000 = 1.395p
Add .1p to both sides: 37000 = 1.495p
Divide by 1.495: 24749.16 = p
She bought the picture for $24749.16.
We can then check our answer by filling out the equation (the 1.125s cancel):
-24749.16 + .9*24749.16 +37000 = 1.395 * 24749.16
-2474.916 +37000 = 34525.0782
34525.084 = 34525.782 (result of rounding answer to pennies before)