A chocolate bar is separated into several equal pieces. If one person eats 1/4 of the pieces, and a second person eats 1/2 of the remaining pieces, there are six pieces left over. Into how many pieces was the original bar divided?

let the number of pieces be x

(1/4)x + (1/2)(1 - (1/4)x) + 6 = x

x/4 + 3x/8 + 6 = x
multiply by 8

2x + 3x + 48 = 8x
x = 16

check
they eat 1/4 of 16, leaving 12
then they eat 1/2 of that , leaving 6

Ms Sue had 24.
eating 1/4 of that leaves 18
eating 1/2 of that would leave 9, not 6

Here is another way to do it.

Let x = number of pieces.
Then x-(1/4)x -(1/2)*(3/4)x = 6
x-(1/4)x-(3/8)x = 6
multiply through by 8 to clear the fractions.
8x-2x-3x=48
3x = 48
x = 16 pieces.
CHECK:
(1/4)*16 = 4 were eaten by person #1.
That leaves 16-4 = 12 pieces.
The second person ate 1/2 of that or (1/2)*12 = 6
So the first person ate 4, the second person ate 6 which makes a total of 10 and that leaves 6 pieces if there were 16 initially.

Oops -- thanks, Reiny.

I didn't read very carefully. I missed the part about eating 1/2 of the REMAINING pieces.

i have no clue, sorry guys. I would help but I don't know. P.S this is not 6th grade math it is 4th grade math since I am in 4th grade i had the same question and my name is not actually Hanna it is...

Younhie and Johnny each have a chocolate bar. Their chocolate bars are of the same size.

Younhie breaks hers into 9 equal pieces. Johnny breaks his into 6 equal pieces. If Younhie eats 3 pieces of her bar, and she and Johnny eat the same amount of chocolate, how many pieces does Johnny eat of his bar?

To solve this problem, let's break it down step by step.

Let's assume that the original chocolate bar was divided into "x" equal pieces.

Step 1: The first person eats 1/4 of the pieces.
This means the first person ate (1/4)*x pieces.

Step 2: After the first person ate, the remaining pieces would be x - (1/4)*x pieces.

Step 3: The second person eats 1/2 of the remaining pieces.
This means the second person ate (1/2)*(x - (1/4)*x) pieces.

Step 4: After the second person ate, there are six pieces left over.
So, the remaining pieces after the second person ate would be (x - (1/4)*x) - (1/2)*(x - (1/4)*x) = 6.

Now, let's solve for "x":

(x - (1/4)*x) - (1/2)*(x - (1/4)*x) = 6

First, let's simplify the equation.

(x - (1/4)*x) - (1/2)*(x - (1/4)*x) = 6

(x - (1/4)*x) - (1/2)*(x - (1/4)*x) = 6

(x - 1/4*x) - 1/2 * (x - 1/4*x) = 6

(4/4 * x - 1/4 * x) - 1/2 * (4/4 * x - 1/4 * x) = 6

(3/4 * x) - 1/2 * (3/4 * x) = 6

(3/4 * x) - 3/8 * x = 6

Now let's combine like terms:

3/4 * x - 3/8 * x = 6

To combine the fractions, we need to find a common denominator. In this case, the least common denominator (LCD) is 8.

3/4 * x - 6/8 * x = 6

Now, let's subtract the two fractions:

(3/4 - 3/8) * x = 6

(6/8 - 3/8) * x = 6

3/8 * x = 6

Finally, let's solve for "x" by dividing both sides of the equation by 3/8:

x = (6) / (3/8)
x = 6 * (8/3)
x = 16

Therefore, the original chocolate bar was divided into 16 equal pieces.

1 - 3/4 = 1/4

1/4 = 6 pieces

4 * 6 = 24

Let's see if that works --

6 + 12 + 6 = 24

Yep, it works!