A certain collector sold 5/8 of her paintings, including 2/3 of her

I picked number to start with. to selected easy number, i multiplied denominators of all fractions, 8*3*5=120, so total nu of painings assumed is 120. She sold a total of 75 painings, while she owned a total of 72 impressionist paintings, out of which she sold 2/3 or 48. So she has the remaining of 24 impress. painings, while total nu is 120-75, 45. so it is 24/45

s

Every painting is EITHER sold OR not sold.
Every painting is EITHER impressionist OR not impressionist.
For an either/or problem, use a DOUBLE-MATRIX to organize the data.

Let S = sold, NS = not sold, I = impressionist and NI = not impressionist.
Let the total number of paintings = the LCM of the 3 denominators in the prompt = 8*3*5 = 120.
The following matrix is yielded:



A certain collector sold \(\frac{5}{8}\) of her paintings.
Since total sold = \(\frac{5}{8} * 120 = 75\), the following matrix is yielded:



\(\frac{3}{5}\) of her paintings were impressionist.
Since total impressionist = \(\frac{3}{5} * 120 = 72\), the following matrix is yielded:



A certain collector sold...\(\frac{2}{3}\) of her impressionist paintings.
Since \(\frac{2}{3}\) of the 72 impressionist paintings = \(\frac{2}{3} * 72 = 48\), the following matrix is yielded:



What fraction of the paintings that were NOT SOLD were impressionist?
In the resulting matrix:
\(\frac{(impressionist-not-sold)}{(total-not-sold)} = \frac{24}{45} = \frac{8}{15}\).

HELLO!
LCM (8, 3, 5) = 120
Sold=120*5/8=75
Impression=120*3/5=72
Imp sold=72*2/3=48
Imp unsold =72-48=24
Unsold=120-75=45
Fr=24/45=8/15

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