Answer:
27/56
Explanation:
Given that the ratio of black shape to white shape cards is 3 : 5, and the ratio of circle to triangle cards is 2 : 7, and the only cards in the game have black or white shapes that are a circle or triangle, you want the ratio of black shape cards to triangle cards.
Fractions
The fraction of total cards with a black shape is 3/(3+5) = 3/8.
The fraction of total cards with triangles is 7/(2+7) = 7/9.
Then the ratio of interest is ...
black shape : triangle = (3/8) : (7/9) = 27 : 56
The number of black shape cards is 27/56 of the number of cards with a triangle.
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Additional comment
The ratio of fractions can be made a ratio of integers by multiplying it by 72, the least common denominator of the two fractions.