Emilio was playing marbles in the first round he lost 1/2 of his marbles in the second round he lost 1/4 of his his remaining marbles in the third round he lost 1/3 of his remaining marbles he gave 1 marble to his friend he had 1 marble left how many marbles did he have when he started the game
If you work backwards (which is a viable problem solving strategy in grade 3 you have).
He gave a marble away and had 1 left.
So... he had 2 marbles.
But before that he had to lose 1/3 of his marbles (and still have 2 left) so... 1/3 of 3 marbles is one marble. 3 - 1 = 2 marbles : )
So working backwards again he had 3 marbles... but lost 1/4 (and ended up with three) So if he had 4 marbles and lost 1/4 that means he would loose 1 and have 3.
So working backwards with the 4 marbles we are on the final round. If he lost half his marbles and ended up with 4 marbles. So half of 8 marbles is 4 marbles... 8=4 = 4 marbles. So he must have started with 8 marbles.
You could also "guess and check" options... much later they will do the same question using algebra and the introduction of the variable x. But in grade 3, working backwards is their best option : )
Hope this helps,
Yours in Mathematical fun, Ms Pi
Well, it seems like Emilio had a pretty marble-ous adventure! Let's break it down. Starting with the final step, we know Emilio had one marble left after all the rounds and giving one to his friend.
Now, if we work backward, we can find out how many marbles he had before giving one away. In the third round, Emilio lost 1/3 of his remaining marbles. So, if we have one marble left at this point, that means he had 1 * 3 = 3 marbles before the third round.
Moving on to the second round, Emilio lost 1/4 of his remaining marbles. Using the same logic, if he had 3 marbles before the second round, he must've had 3 * 4 = 12 marbles before the second round.
And finally, in the first round, Emilio lost 1/2 of his marbles. Since he had 12 marbles before the first round, we can conclude that Emilio must've started the game with 12 * 2 = 24 marbles.
So, our final answer is that Emilio started the game with 24 marbles. Don't worry, Emilio, even if you lost a few along the way, you still had a ball with those marbles!
Let's solve this problem step-by-step.
Let's assume that Emilio had "x" marbles originally.
In the first round, he lost 1/2 of his marbles, which means he had (x - (1/2)x) = (1/2)x marbles remaining.
In the second round, he lost 1/4 of his remaining marbles, which means he had ((1/2)x - (1/4)(1/2)x) = ((1/2)x - (1/8)x) = (3/8)x marbles remaining.
In the third round, he lost 1/3 of his remaining marbles, which means he had ((3/8)x - (1/3)(3/8)x) = ((3/8)x - (1/8)x) = (2/8)x = (1/4)x marbles remaining.
After giving 1 marble to his friend, he had (1/4)x - 1 marbles remaining.
According to the given information, he had 1 marble left, so we can set up the equation:
(1/4)x - 1 = 1
Adding 1 to both sides of the equation, we get:
(1/4)x = 2
Multiplying both sides of the equation by 4, we get:
x = 8
So, Emilio had 8 marbles when he started the game.
To find out how many marbles Emilio had when he started the game, let's work through the problem step by step.
1. In the first round, he lost 1/2 of his marbles. Let's say he had M marbles initially. After the first round, he had 1/2M marbles left.
2. In the second round, he lost 1/4 of his remaining marbles. So, after the second round, he had 3/4 * 1/2M = 3/8M marbles left.
3. In the third round, he lost 1/3 of his remaining marbles. Therefore, after the third round, he had 2/3 * 3/8M = 1/4M marbles left.
4. Emilio then gave 1 marble to his friend, leaving him with 1/4M - 1 marble.
5. Finally, we know that Emilio had 1 marble left after all the rounds and giving one to his friend. So, 1/4M - 1 = 1.
To find the value of M (the number of marbles he initially had), we can solve for M:
1/4M - 1 = 1
1/4M = 2
M = 2 * 4
M = 8
Therefore, Emilio had 8 marbles when he started the game.