Question

Select all that apply.Several pennies are tossed in the air. Twelve land heads up and fifteen land tails up. Which of the following ratios are correct?
12 heads to 27 coins

15 tails to 12 heads

5 tails to 9 coins

12 heads to 15 tails

Answer 1

The answer is the last one: twelve heads to fifteen tails. After all, those are the two numbers mentioned, right?

Answer 2

The information we've been given is:

12 heads
15 tails

From those, we find that there are 12 + 15 = 27 coins.

Let's examine these ratios as such:

- 12 heads to 27 coins -
There are indeed 12 heads and 27 coins, so this comparison agrees with our data.

- 15 tails to 12 heads - 
Again, nothing here contradicts with our data, so this would be correct as well

- 12 heads to 15 tails -
Simply a reversed version of the ratio above; still a completely valid way to compare the relative quantities of heads and tails

- 5 tails to 9 coins -
This one needs a little more examination. We observe that the ratio of tails to coins with our given data is 15 tails to 27 coins. This seems to go against our data, but we can simplify our ratio by dividing both the number of tails and the number of coins by 3, which indeed gives us the ratio 5 tails to 9 coins.

So, all of the given ratios are correct.