1) If this pattern continues, in which column will 500 appear?
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This problem involves arithmetic sequences.
1. Notice that in each column the next number is the previous number + 9.
Don't worry about the blank spaces.
2. Compute which element of the sequence that 500 will occur in by dividing it by 9 = 55.55th element.
If this is not an even number, round up = 56th element.
3. The formula for finding the nth element of an arithmetic sequence is:
An = A1 + D x (n - 1)
where D is the amount added to each element
4. Using this formula (your An is 500), find the column with the appropriate starting number that makes the 56th element 500.
500 = X + 9 X 55
X = 500 - 495 = 5. The first element is 5.
5. That number occurs as the first element in column I
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2) Jimmy and Carlos are at a meeting with eight other people. They are all hungry, but there are only seven bagels. Jimmy divides each bagel in half and gives each person a half of a bagel. He takes the remaining pieces and keeps dividing them all in half until he can again give everyone an equal size piece. He repeats this again with the remaining pieces he now has until everyone has gotten 3 of the same size pieces, a large piece, a medium piece and a small piece. If Jimmy takes his fair share and any remaining pieces, what fraction of the bagels does Jimmy get? Express your answer to the nearest 1/16th of
a bagel. |
1. There are 7 bagels making 14 half-bagels.
2. After passing out 10 half-bagels, there are 4 half-bagels left which he cuts in half to make 8 quarter-bagels
3. After passing these out there is 1 quarter-bagel left, which he cuts in half to make 2 eighth-bagels
4. This cannot be passed to 10 people, so he cuts it again into 4 sixteenth bagels, and then 8 thirty-second bagels.
5. He passes out 7 of the thirty-second bagels, leaving 1 thirty-second bagel left, which is his.
6. So, each person got 1 half-bagel, 1 quarter-bagel and 1 thirty-second bagel, leaving 1 thirty-second bagel left, which is his.
7. So, Jimmy got what everyone else got: 1 half, 1 quarter and 1 32nd bagel plus a second 32nd bagel which sums to
16/32 + 8/32 + 2/32 = 26/32 = 13/16th of a bagel.
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