, 2025

Solution 1:

We begin by recognizing that written as a fraction in lowest terms,
$60\%$ is equal to $\dfrac35$.

Thus, if Savanah tossed $3$ tails out
of $5$ tosses, then $60\%$ of the tosses that she made were
tails.

Since the result of her last toss was tails, then following Savanah’s
second last toss she had tossed $2$
tails out of $4$ tosses, meaning that
$50\%$ of the tosses that she made to
that point were tails, as required.

Therefore, Savanah made $5$ tosses in
total.

Solution 2:

We proceed to work backward from the answers given.

If Savanah made $3$ tosses, and 60%
of those tosses were tails, then she tossed $3\times\dfrac{60}{100}=\dfrac{180}{100}=1.8$
tails. She must toss a whole number of tails, and so this is not
possible.

If Savanah made $9$ tosses, then she
tossed $9\times\dfrac{60}{100}=\dfrac{540}{100}=5.4$
tails. Again, this is not possible.

If Savanah made $8$ tosses, then her
second last toss was her 7th toss. However, it is not possible for
Savanah to toss $50\%$ tails in $7$ tosses (since one half of $7$ is not a whole number). (We could have
instead shown that $60\%$ of $8$ is also not an integer as we did in the
first two cases.)

Similarly, Savanah could not have made $10$ tosses since one half of $9$ tosses is not an integer.

By process of elimination, the answer must be $5$ tosses. We can confirm that if she
tosses $2$ tails in her first $4$ tosses, then $50\%$ of her tosses are tails, and if her
final toss is a tail, then she has tossed $3$ tails out of $5$ tosses, which is $60\%$ tails, as required.