Math Snap

STEP 1

Assumptions1. The prizes are powers of, starting from $1,$, $4,$8, $16,$32, $64,$128, $256,$512.
. The total amount to be distributed is $988.
3. We need to distribute the prizes in such a way that the total amount is used up, and the number of prizes is minimized.

STEP 2

First, we need to find the largest power of2 that is less than or equal to the total amount. This will be the first prize.
Prize1 = \($\)512

STEP 3

Subtract the first prize from the total amount to find the remaining amount.
$$Remaining\, amount = Total\, amount - Prize1$$

STEP 4

Plug in the values for the total amount and the first prize to calculate the remaining amount.
Remaining\, amount = \($\)988 - \($\)512

STEP 5

Calculate the remaining amount.
Remaining\, amount = \($\)988 - \($\)512 = \($\)476

STEP 6

Repeat the process of finding the largest power of2 that is less than or equal to the remaining amount. This will be the second prize.
Prize2 = \($\)256

STEP 7

Subtract the second prize from the remaining amount to find the new remaining amount.
$$New\, remaining\, amount = Remaining\, amount - Prize2$$

STEP 8

Plug in the values for the remaining amount and the second prize to calculate the new remaining amount.
New\, remaining\, amount = \($\)476 - \($\)256

STEP 9

Calculate the new remaining amount.
New\, remaining\, amount = \($\)476 - \($\)256 = \($\)220

STEP 10

Continue this process until the remaining amount is0. The prizes are $512,$256, $128,$64, $16,$8, $4.

Count the number of prizes to find the minimum number of prizes that could be distributed.
$$Number\, of\, prizes =7$$The minimum number of prizes that could be distributed from $988 is7.