Brain Teaser?

Question

At the local candy store, three delicious candies are on sale.
A Sweetie, a Yummie and a Tastie together cost $.40.
A Tastie is over three times the price of a Sweetie.
Six Sweeties are worth more than a Yummie.
A Tastie, plus two Sweeties costs less than a Yummie.
Can you determine the price of each type of candy?

Tell how you got your answer.

Answer 1

first get rid of he candies and the shop

this is what you have to solve then

x + y + z = 40
x - 3y = 0
6y > z
x + 2y < z

with x,y,z integers.

Answer 2

One solution, at least is $0.04, $0.13 and $0.23:

Call the cost of the candies s, t and y in cents (based on first letters)

From the first statement we get the following expression:
s + t + y = 40

From the second: t > 3s

From the third: 6s > y

From the fourth: t + 2s < y

Now, combine the third and fourth: 6s > y > t + 2s

From the second, and adding 2s, we get:

t > 3s so t + 2s > 5s

So, in total we get: 6s > y > t + 2s > 5s

From this, and the fact that I'm assuming candies can cost only integer number of pennies, s >= 3 or 6s cannot be three strict inequality steps greater than 5s.

I tried s = 3. Didn't work. Too much typing to go through here.

s = 4:

From t > 3s, I know that t > 12.

From 6s > t + 2s > 5s and with s = 4 I get that:

t + 8 > 20 ==> t > 12

Trying t = 13:

s + t + y = 40, s = 4 and t = 13 ==> y = 23

Putting this all into the master inequality:

6s > y > t + 2s > 5s
24 > 23 > 21 > 20 so it checks out.

Haven't checked if the solution is unique, however.