SOLUTION: Alex, Benjamin and Caris shared some pancakes. Caris took {{{3/4}}} of the pancakes and {{{1/4}}} of a pancake. Benjamin took {{{3/4}}} of the remaining number of pancakes and {{

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Alex, Benjamin and Caris shared some pancakes. Caris took {{{3/4}}} of the pancakes and {{{1/4}}} of a pancake. Benjamin took {{{3/4}}} of the remaining number of pancakes and {{      Log On


   

Question 1185291: Alex, Benjamin and Caris shared some pancakes. Caris took 3%2F4 of the
pancakes and 1%2F4 of a pancake. Benjamin took 3%2F4 of the remaining number of
pancakes and 1%2F4 of a pancake. There were only 6 pancakes left for Alex.
How many pancakes were there at first?
Found 3 solutions by josgarithmetic, MathTherapy, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
p, original number of the pancakes

(1)
Three fourths plus one fourth of the pancakes taken, the remains become
p%2F4-1%2F4.

(2)
Ben took three quarters of that and one quarter of a pancake, so what remains is
%281%2F4%29%28p%2F4-1%2F4%29-1%2F4.


Six pancakes remained for Alex.
%281%2F4%29%28p%2F4-1%2F4%29-1%2F4=6------simplify and solve this for p.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
Alex, Benjamin and Caris shared some pancakes. Caris took 3%2F4 of the
pancakes and 1%2F4 of a pancake. Benjamin took 3%2F4 of the remaining number of
pancakes and 1%2F4 of a pancake. There were only 6 pancakes left for Alex.
How many pancakes were there at first? 
Let original number of pancakes be P
After Caris took 3%2F4 of original number of pancakes, plus %281%2F4%29%5E%28th%29 of a pancake,  pancakes were left
After Benjamin took 3%2F4 of the remaining number of pancakes, plus %281%2F4%29%5E%28th%29 of a pancake,  were left
With 6 pancakes remaining in the end, we get: matrix%281%2C3%2C+%28P+-+5%29%2F16%2C+%22=%22%2C+6%29
P - 5 = 96 ------ Cross-multiplying

Original number of pancakes, or 

You can do the CHECK!!

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Sometimes problems like this are easier to work "forwards", as the other tutors did; sometimes they are easier to work backwards.

This problem seems much easier to work backwards.

Each time someone takes "and 1/4 of a pancake", working backwards that adds 1/4 pancake to the total.

And each time someone takes 3/4 of the remaining pancakes, it means he left 1/4 of the remaining pancakes, so working backwards it mean multiplying the number of pancakes by 4.

So....

At the end: 6 pancakes
Before the last time 1/4 pancake was taken: 6+1/4 = 6 1/4
Before the last time 3/4 of the pancakes were taken: 4*(6 1/4) = 25
Before the last time 1/4 pancake was taken: 25+1/4 = 25 1/4
Before the last time 3/4 of the pancakes were taken: 4*(25 1/4) = 101

ANSWER: There were 101 pancakes originally