A chocolate bar is separated into several equal pieces. If one person eats
one quarter of the pieces and a second person eats one half of the
remaining pieces, there are six pieces left over. Into how many pieces was
the original bar divided?
1/4 + 1/2 * 3/4 = 5/8 eaten
so, 3/8 x = 6
Let's solve this problem step-by-step:
1. Let's assume the original number of pieces in the chocolate bar is represented by 'x'.
2. The first person eats one-quarter of the pieces, which means they eat (1/4) * x = x/4 pieces.
3. After the first person eats their share, the remaining number of pieces is (x - x/4) = (3x/4).
4. The second person eats one-half of the remaining pieces, which means they eat (1/2) * (3x/4) = (3x/8) pieces.
5. After the second person eats their share, the remaining number of pieces is (3x/4 - 3x/8) = (3x/8).
6. According to the problem, there are 6 pieces left over, so we can set up the following equation:
(3x/8) = 6
7. To solve for 'x', we can multiply both sides of the equation by 8:
3x = 48
8. Dividing both sides by 3 gives us:
x = 16
Therefore, the original chocolate bar was divided into 16 equal pieces.
To solve this problem, let's work through it step by step.
Let's first assume that the original chocolate bar was divided into "x" equal pieces.
The first person eats one quarter of the pieces, which is equal to x/4 pieces.
After the first person eats, there will be (x - x/4) = (3x/4) pieces remaining.
The second person eats one half of the remaining pieces, which is equal to (3x/4)/2 = 3x/8 pieces.
After the second person eats, there will be (3x/4 - 3x/8) = (3x/8) pieces remaining.
We are given that there are 6 pieces left over. Therefore, (3x/8) = 6.
To find the value of x, we can multiply both sides of the equation by 8/3:
(8/3) * (3x/8) = (8/3) * 6
This simplifies to:
x = 16
So the original chocolate bar was divided into 16 equal pieces.