SOLUTION: Three algebra students were doing their homework together. As a treat, one mom offered to bake some cookies. While waiting for the to cool, all three students fell asleep. After a

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Three algebra students were doing their homework together. As a treat, one mom offered to bake some cookies. While waiting for the to cool, all three students fell asleep. After a       Log On


   

Question 1020626: Three algebra students were doing their homework together. As a treat, one mom offered to bake some cookies. While waiting for the to cool, all three students fell asleep. After a while, Latisha woke up and ate what she thought was her equal share of cookies. She later went back to sleep. Soon after, Susan woke up, ate what she thought was her equal share, and fell asleep again. Then Hieu woke up, ate what she thought was her share, and went back to sleep. Later, all three kids woke up and discovered 8 cookies left. How many cookies were baked originally?
B)The next day, four students got together to study. Another mom baked cookies. Again the four students fell asleep. As before, they woke up one at a time and each ate her equal share. When they all awakened, they discovered 81 cookies remained. How many were baked originally?
Thank you so much. I just need help on part b so if you could help that would be awesome!
Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
Three algebra students were doing their homework together. As a treat, one mom offered to bake some cookies. While waiting for the to cool, all three students fell asleep. After a while, Latisha woke up and ate what she thought was her equal share of cookies. She later went back to sleep. Soon after, Susan woke up, ate what she thought was her equal share, and fell asleep again. Then Hieu woke up, ate what she thought was her share, and went back to sleep. Later, all three kids woke up and discovered 8 cookies left. How many cookies were baked originally?
B)The next day, four students got together to study. Another mom baked cookies. Again the four students fell asleep. As before, they woke up one at a time and each ate her equal share. When they all awakened, they discovered 81 cookies remained. How many were baked originally?
Thank you so much. I just need help on part b so if you could help that would be awesome!
2nd is the same as 1st

Only difference is there were 4 students then, compared to 3 in (a)



As there are 4, each person's perceived share is: 1%2F4

1st student to eat eats: 1%2F4 leaving a remainder of 3%2F4

2nd student to eat eats: 1%2F4 of remainder, or 1%2F4 of 3%2F4, leaving matrix%281%2C3%2C3%2F4%2C+of%2C+3%2F4%29, or 9%2F16

3rd student to eat eats: 1%2F4 of remainder, or 1%2F4 of 9%2F16, leaving matrix%281%2C3%2C3%2F4%2C+of%2C+9%2F16%29, or 27%2F64

Finally, the 4th student to eat eats: 1%2F4 of remainder, or 1%2F4 of 27%2F64, leaving matrix%281%2C3%2C3%2F4%2C+of%2C+27%2F64%29, or 81%2F256.

This remainder represents the 81 cookies that were uneaten, and with C being the original number of

cookies, the result is the proportion: %2881%2F256%29%2F1+=+81%2FC

81C%2F256+=+81 ---------- Cross-multiplying

81C+=+256%2881%29 ---- Cross-multiplying 

C, or original number of cookies = 256%2881%29%2F81 ------> 256cross%28%2881%29%29%2Fcross%2881%29%29, or highlight%28highlight_green%28highlight%28256%29%29%29



You could've also worked backwards to get the original number of cookies. I'll leave that up to you to

explore, especially if it's easier for you!