Alex ate 1/3 of a box of cookies. Then Beth ate 1/4 of what was left after Alex had finished. Finally, Carmine ate 1/5 of what was left after Beth had finished. When Carmine was done, only 36 cookies were left. How many cookies were in the box originally?
Alex ate 1/3, leaving 2/3
Beth ate 1/4 * 2/3 = 1/6, leaving 1/2
Carmine ate 1/5 * 1/2 = 1/10, leaving 2/5
so, 2/5 x = 36
x = 90
Ah, the case of the disappearing cookies! Let's put on our detective hats and solve this cookie conundrum.
First, let's break it down. Alex devoured 1/3 of the cookies, leaving us with 2/3. Then, Beth swooped in and munched on 1/4 of the remaining cookies. That brings us down to 3/4 × 2/3, which is... hmm, let me grab my handy clown calculator... got it! We're left with 1/2 of the original number of cookies.
But the cookie madness doesn't end there! Carmine joined the party and gobbled up 1/5 of what Beth left behind. That leaves us with 4/5 × 1/2 of the original cookies. Excuse me while I whip out my juggling pins... got it! We're left with 4/10 of the original number of cookies.
Now, we know that these 4/10 of the original cookies amount to 36 cookies. So, let's do some arithmetic magic. If 4/10 is equal to 36, we can multiply both sides by 10/4 to find out the original number of cookies.
Grab your balloon animals because the original number of cookies is... *drumroll* 90 cookies! Ta-da!
So, it seems there were initially 90 cookies in that elusive box. Hopefully, this mystery has been solved and I've given you a good chuckle along the way!
Let's suppose there were x cookies in the box initially.
After Alex ate 1/3 of the cookies, there were (2/3)x cookies left.
Beth then ate 1/4 of what was left after Alex had finished. Therefore, there were (3/4)((2/3)x) = (1/2)x cookies left after Beth ate.
Finally, Carmine ate 1/5 of what was left after Beth had finished. So, there were (4/5)((1/2)x) = (2/5)x cookies left after Carmine ate.
According to the given information, only 36 cookies were left, so we can set up an equation:
(2/5)x = 36
To solve for x, we can multiply both sides of the equation by 5/2:
x = 36 * (5/2)
x = 90
Therefore, there were initially 90 cookies in the box.
To find the original number of cookies in the box, we can work backwards by following the instructions provided in the question.
Let's first find the number of cookies remaining after Carmine had finished. We know that there were only 36 cookies left at that point. Let's call the number of cookies remaining after Beth had finished as "x."
Since Carmine ate 1/5 of what was left after Beth had finished, we can use the equation:
x - (1/5)x = 36
Simplifying the equation gives us:
(4/5)x = 36
To isolate x, we can multiply both sides of the equation by 5/4:
x = (36)(5/4)
x = 45
So, there were 45 cookies remaining after Beth had finished.
Now, let's find the number of cookies remaining after Alex had finished. We know that Beth ate 1/4 of what was left after Alex had finished. So, we can use the equation:
x - (1/4)x = 45
Simplifying the equation gives us:
(3/4)x = 45
To isolate x, we can multiply both sides of the equation by 4/3:
x = (45)(4/3)
x = 60
Therefore, there were 60 cookies remaining after Alex had finished.
Now let's calculate the original number of cookies. We know Alex ate 1/3 of the box, so the fraction left after Alex ate would be 1 - 1/3, which is 2/3.
Let's call the original number of cookies as "N." We can use the equation:
(N)(2/3) = 60
To isolate N, we can multiply both sides of the equation by 3/2:
N = (60)(3/2)
N = 90
Therefore, the original number of cookies in the box was 90.