calculus II

posted by .

(A) 2 students are sharing a loaf of bread. Student A eats half of the loaf, then student B eats half of what remains, then student A eats half of what remains, and so on. How much of the loaf will each student eat?

(B) 2 students are sharing a loaf of bread. Student A eats 2/3 of the loaf, then student B eats half of what remains, then student A eats 2/3 of what remains, then student B eats half of what remains, and so on. How much of the loaf will each student eat?

(3) 3 students decide to share a loaf of bread. Student A eats half of the loaf, passes what remains to student B who eats half, and then onto student C who eats half, and then back to student A who eats half, and so on. How much of the loaf will each student eat?

* calculus II - Reiny, Sunday, April 11, 2010 at 9:18pm

make 2 columns, marked A and B
A eats 1/2 leaving 1/2 -- B eats 1/4 leaving 1/4
A eats 1/8 th leaving 1/8th -- B eats 1/16 th, leaving 1/16 th

So A eats 1/2 + 1/8 + 1/32 + ...
a Geometric series with a=1/2, r = 1/4
S∞ = a/(1-r) = (1/2)/(1 - 1/4)
= (1/2)/(3/4) = 2/3

So A eats 2/3 of the loaf

The clearly B must eat the missing parts or 1/3.

Do the others the same way.

* calculus II - Harold, Wednesday, April 14, 2010 at 12:33am

All I need to know is how do you do part two (2)? Is there a summation formula that we can use?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Maths

    Trudy brought a large bag of wine gums to school. She gave half to the first student she met, half the remainder to the next and half of what she had left to the third student. The last 5 wine gums she ate. How many were in the packet?
  2. 6 th grade math

    2 students are learning how to bake apple and blueberry pies. The first student makes an apple pie and the second student bakes a blueberry pie. If the first student eats 1/4 of the apple pie and the second student eats 1/2 of the …
  3. calculus II

    (A) 2 students are sharing a loaf of bread. Student A eats half of the loaf, then student B eats half of what remains, then student A eats half of what remains, and so on. How much of the loaf will each student eat?
  4. math 2nd grade

    Dwayne eats 1/9 of the raisin bread. Francisco eats 1/3 of the raisin bread. Who eats more raisin bread?
  5. maths

    Robert cut 3 4 of a loaf of bread in half. Which equation can be used to determine the fraction of the whole loaf represented by each piece n ?
  6. CALC 2

    B. 2 students are sharing a loaf of bread. Student A eats 2/3 of the loaf, then student B eats half of what remains, then student A eats 2/3 of what remains, then student B eats half of what remains, and so on. How much of the loaf …
  7. Math

    Leena bakes a loaf of bread. She eats 1/8 loaf of bread and give 1/6 of it each of her 3 friends. What fraction of the loaf of bread is left?
  8. Math

    Leena bakes a loaf of bread. She eats 1/8 of the loaf and gives 1/6 of it to each of her 3 friends. What fraction of the loaf of bread is left?
  9. Fractions

    how many pizzas are required if mario eats 1/3 of a pizza, Luigi eats 3/5 of a pizza, and Bruno eats 1 1/4?
  10. Math

    Marcus bake loaf of bread of banana bread for a party he cut the loaf into equal size . At the end of the party there were 6 pieces left . Explain how you can find the number of pieces in the whole loaf if Marcus told 1/3 of the loaf …

More Similar Questions