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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?

• 6th grade math - ,

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!

• 6th grade math - ,

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

eating 1/4 of that leaves 18
eating 1/2 of that would leave 9, not 6

• 6th grade math - ,

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.

• 6th grade math - ,

Oops -- thanks, Reiny.

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