Adam, Bryant and Clara shared some pies. Adam ate 2/3 of the number of pies
and 2/3 of a pie. Bryant then ate 2/3 of the remaining number of pies and 2/3 of a
pie. Finally, after Bryant had eaten his pies. Clara ate 2/3 of the remaining
number of pies and 2/3 of a pie. There was no pie left.
(a) How many pies were there at first?
(b) How many pies did Bryant eat?
very confusing pie eating event.
Assume all the pies are the same , let x represent the number of pies
Adam ate: (2/3)(x) + (2/3) = (2/3)(x + 1)
Pies left = x - (2/3)(x+1)
= x - 2/3 x - 2/3 = 1/3 x - 2/3 = (x-2)/3
Bryant ate: (2/3)(x-2)/3 + 2/3
= 2/9 x - 4/9 + 2/3
= 2/9 x + 2/9
pies left over after that:
= (1/3 x - 2/3) - (2/9 x + 2/9)
= 1/9 x - 8/9
Clara ate: (2/3)((1/9 x - 8/9) + 2/3
= 2/27 x - 16/27 + 2/3
= 2/27 x + 2/27
pies left over after that
= 1/9 x - 8/9 - 2/27 x - 2/27
= 1/27 x - 26/27
this is supposed to be equal to zero
1/27 x = 26/27
x = 26
so we started with 26 pies, and Bryant ate
2/9 x + 2/9
= (2/9)(26) + 2/9 = 6 pies
Thank u very much
Let number of pies = X
Adam : 2/3X + 2/3
Bryant : 2/5 (X-Adam) + 2/3
= 2/3 (1/3x - 2/3) + 2/3
= 2/9x - 4/9 + 6/9 = 2/9x + 2/9
Clara = 2/3 (X-Adam-Bryant) + 2/3
= 2/3 (1/3x - 2/3 - 2/9x - 2/9) + 2/3 = 2/3 (1/9x - 8/9) + 2/3
= 2/27x + 2/27
A + B + C = 2/27x + 2/27 + 2/9x + 2/9 + 2/3x + 2/3 = x
26/27x + 26/27 = x
1/17x = 26/27
X = 26 (a)
(2/9)(26)+2/9 = 6 (b)
To solve this problem, we can start by working backwards. We know that after Clara ate her share, there were no pies left. So, we can figure out how many pies Clara ate and use that information to determine how many pies were there at first.
Let's go step by step:
Step 1: Clara's share
After Bryant ate his share, there were no pies left. Therefore, Clara ate 2/3 of the remaining number of pies and 2/3 of a pie.
Let's represent the number of pies Clara ate as C. We can write this as an equation:
C = (2/3)(R - 2/3) + 2/3
Simplifying this equation, we get:
C = 2/3R - 4/9 + 2/3
Combining like terms, we get:
C = 2/3R + 2/9
Step 2: Bryant's share
Before Clara ate her share, there were some pies left. Bryant ate 2/3 of the remaining number of pies and 2/3 of a pie.
The number of pies Bryant ate is given as B. We can write this as an equation:
B = (2/3)(R - 2/3) + 2/3
Simplifying this equation, we get:
B = 2/3R - 4/9 + 2/3
Combining like terms, we get:
B = 2/3R + 2/9
Step 3: Total pies at first
Since there were no pies left after Clara ate her share, we can write an equation for the total number of pies:
R = C + B + (2/3)
Substituting the expressions we found for C and B, we have:
R = (2/3R + 2/9) + (2/3R + 2/9) + (2/3)
Simplifying this equation, we get:
R = 2/3R + 2/9 + 2/3R + 2/9 + 2/3
Combining like terms, we get:
R = (4/3)R + (4/9) + (2/3)
To solve for R, we can eliminate the fractions by multiplying both sides of the equation by 9 to get rid of the denominators:
9R = 12R + 4 + 6
Simplifying this equation, we get:
9R - 12R = 10
-3R = 10
Now, we can solve for R by dividing both sides of the equation by -3:
R = -10/3
Since we can't have a negative number of pies, this indicates that there is no solution to the problem. Thus, there is an inconsistency in the given problem statement.
Hence, we cannot determine the initial number of pies or the number of pies Bryant ate with the given information.