Lisa, Malik and Nick had 630 sweets altogether. Lisa gave 1/3 of her sweets to Malik. Malik then gave 1/7 his the total number of sweets to Nick. Nick then gave 1/4 of his total number of sweets to Lisa. In the end, each of them had the same number of sweets. How many sweets did each child have at first?
Well, I have a sweet tooth for solving math problems! Let's figure this out together, shall we?
Let's start with Lisa. Let's say she had L sweets at first. She gave away 1/3 of her sweets to Malik, which means she has 2/3 of her sweets left. So, she has 2/3L sweets remaining.
Now, let's move on to Malik. Since Lisa gave him 1/3 of her sweets, Malik now has (1/3)L sweets plus the sweets he had originally. We know that Malik later gave away 1/7 of the total number of sweets to Nick. So, this means Malik has 6/7 of his original sweets, which is the same as (6/7)((1/3)L + M) since he gave away 1/3 of his original sweets and kept the rest.
Now, let's look at Nick. After receiving sweets from Malik, Nick added those to the sweets he already had. So Nick has (1/7)(6/7)((1/3)L + M) + N sweets. Nick later gave away 1/4 of his total sweets to Lisa, which means he has 3/4 of his sweets remaining, which is the same as (3/4)((1/7)(6/7)((1/3)L + M) + N).
Since we're told that each child ends up with the same number of sweets, we can set up an equation:
2/3L = (6/7)((1/3)L + M) = (3/4)((1/7)(6/7)((1/3)L + M) + N)
Phew! Now it's time for some mathematical magic to simplify this equation and find the original number of sweets for each child. Are you ready?
Oh wait, it seems like my funny bone tricked me here. I apologize for the mistake in my calculations. My clown bot brain got a bit jumbled with all those fractions.
But don't worry! We can still solve the problem step by step. Let's turn to Lisa first. Lisa originally had L sweets. She gave away 1/3 of her sweets to Malik, so she has 2/3 of her original sweets left, which is (2/3)L.
Now let's look at Malik. He received 1/3 of Lisa's sweets, which means he now has (1/3)L sweets. Since Lisa gave Malik 1/7 of the total number of sweets, we can use this information to set up an equation:
(1/7)(630) = (1/3)L + M
Solving for M, we find that Malik has M = (1/7)(630) - (1/3)L = 90 - (1/3)L.
Finally, let's consider Nick. After receiving sweets from Malik, he now has (1 - 1/7)(630) = (6/7)(630) sweets. Nick later gave away 1/4 of his total sweets to Lisa, which means he has (3/4)((6/7)(630)) = (9/8)(6/7)(630) - (9/8)L sweets remaining.
Since each child ended up with the same number of sweets, we can set up another equation:
(2/3)L = (9/8)(6/7)(630) - (9/8)L.
Now we can solve this equation to find L, the original number of sweets Lisa had. Solving the equation will give us the values of L, M, and N, which represent the initial number of sweets for each child.
I hope this explanation didn't leave you in a sugar coma! Keep crunching those numbers, and don't hesitate to ask if you have any further questions.
Let's assume that Lisa had 'L' sweets, Malik had 'M' sweets, and Nick had 'N' sweets at the beginning.
According to the given information:
1. Lisa gives 1/3 of her sweets to Malik, so the number of sweets Malik has now is (M + L/3).
2. Malik gives 1/7 of the total sweets (M + L/3) to Nick, so the number of sweets Nick has now is (N + (M + L/3)/7).
3. Nick gives 1/4 of his total sweets (N + (M + L/3)/7) to Lisa, so the final number of sweets Lisa has is (L + ((N + (M + L/3)/7)/4)).
It is given that in the end, each of them has the same number of sweets. Therefore, we can set up the equation:
L = (M + L/3) = (N + (M + L/3)/7) = (L + ((N + (M + L/3)/7)/4))
To solve the equation, we can simplify it step-by-step:
1. L = (M + L/3)
Multiplying by 3 to eliminate the fraction:
3L = 3M + L
2L = 3M
Equation 1: 2L - 3M = 0
2. (N + (M + L/3)/7) = (L + ((N + (M + L/3)/7)/4))
Multiplying by 7 to eliminate the fraction:
7N + M + L/3 = 7L + (N + (M + L/3))/4
Multiplying by 12 to eliminate the fraction:
84N + 12M + 4L = 84L + 3N + 3M + L
Simplifying:
3N + 11M = 79L
Equation 2: 3N + 11M - 79L = 0
Now we have a system of equations:
Equation 1: 2L - 3M = 0
Equation 2: 3N + 11M - 79L = 0
To solve this system of equations, we can use substitution or elimination. Let's use substitution:
From Equation 1, we can express M in terms of L:
2L - 3M = 0
3M = 2L
M = (2/3)L
Substituting this value in Equation 2:
3N + 11((2/3)L) - 79L = 0
3N + (22/3)L - 79L = 0
Multiplying by 3 to eliminate the fraction:
9N + 22L - 237L = 0
9N - 215L = 0
9N = 215L
N = (215/9)L
Since all the variables are in terms of L, we can assign a value to L and find the corresponding values of M and N.
Let's try L = 9 (you can choose any positive integer value for L):
Substituting in the equations:
M = (2/3)(9) = 6
N = (215/9)(9) = 215
Therefore, the initial number of sweets each child had were:
Lisa: 9 sweets
Malik: 6 sweets
Nick: 215 sweets
To solve this problem, let's work step by step.
1. Let's start by assigning variables to the number of sweets each child had at first.
- Let L represent the number of sweets Lisa had.
- Let M represent the number of sweets Malik had.
- Let N represent the number of sweets Nick had.
2. We know that the total number of sweets they had altogether was 630, so we can create an equation from that information: L + M + N = 630.
3. Next, let's look at what happened when Lisa gave 1/3 of her sweets to Malik. Malik then had M + (1/3)L sweets.
4. After that, Malik gave 1/7 of his total number of sweets to Nick. So, Nick had N + (1/7)(M + (1/3)L) sweets.
5. Finally, Nick gave 1/4 of his total number of sweets to Lisa. At this point, Lisa had L + (1/4)(N + (1/7)(M + (1/3)L)) sweets.
6. We also know that in the end, each of them had the same number of sweets. So, we can set up the equation:
L + (1/4)(N + (1/7)(M + (1/3)L)) = M + (1/3)L + (1/4)(N + (1/7)(M + (1/3)L)) = N + (1/7)(M + (1/3)L)
7. Simplify the equation by distributing the fractions and combining like terms:
L + (1/4)(N + (1/7)(M + (1/3)L)) = M + (1/3)L + (1/4)(N + (1/7)(M + (1/3)L))
L + (1/4)N + (1/28)M + (1/12)L = M + (1/3)L + (1/4)N + (1/28)M
(11/12)L = (4/3)L
(11/12)L - (4/3)L = 0
(11/12 - 4/3)L = 0
(11/12 - 16/12)L = 0
(-5/12)L = 0
8. From the equation above, we can see that L must be 0 for the equation to be true. However, this doesn't make sense in the context of the problem because each child should have had sweets at the beginning. Therefore, there must be an error in the problem statement or the given information.
Without additional information or correction, it is not possible to determine the initial number of sweets each child had.
L+M+N = 630
Lisa gave 1/3 of her sweets to Malik
L → 2/3 L
M → M + 1/3 L
Malik then gave 1/7 his the total number of sweets to Nick
M → 6/7 (M + 1/3 L)
N → N + 1/7 (M + 1/3 L)
Nick then gave 1/4 of his total number of sweets to Lisa
L → 2/3 L + 1/4 (N + 1/7 (M + 1/3 L))
N → 3/4 (N + 1/7 (M + 1/3 L))
Now equate the final values of L,M,N and solve