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We can fix the number of chocolate cones in each ratio.

- The actual ratio of v to c was 8 to 12
- If we increase v by 4, the ratio becomes 9 to 12

So increasing the number in the ratio by 1 corresponds to an actual increase of 4, and so our actual numbers must be 4 times what they are in our ratio: we have 32 vanilla and 48 chocolate cones.
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The Binary Ice Cream Shoppe sells two flavors, vanilla and chocolate. On friday, the ratio of vanilla cones sold to chocolate cones sold was 2 to 3. If the store had sold 4 more vanilla cones, the ratio of vanilla cones sold to chocolate cones sold would have been 3 to 4. How many vanilla cones did the store sell on Friday?

A) 32
B) 35
C) 42
D) 48
E) 54

We can create the ratio:

vanilla : chocolate = 2x : 3x

Had the store sold 4 more vanilla cones, the ratio of vanilla cones sold to chocolate cones sold would have been 3 to 4. So we can create the equation:

(2x + 4)/3x = 3/4

4(2x + 4) = 9x

8x + 16 = 9x

16 = x

Thus, the store sold 32 vanilla cones on Friday.

Answer: A
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