QuestionWhat is the minimum number of prizes, all powers of 2, needed to total \$ 988?
Studdy Solution
STEP 1
Assumptions1. The prizes are powers of, starting from , 8, 32, 128, 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.
STEP 3
Subtract the first prize from the total amount to find the remaining amount.
STEP 4
Plug in the values for the total amount and the first prize to calculate the remaining amount.
STEP 5
Calculate the remaining amount.
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.
STEP 7
Subtract the second prize from the remaining amount to find the new remaining amount.
STEP 8
Plug in the values for the remaining amount and the second prize to calculate the new remaining amount.
STEP 9
Calculate the new remaining amount.
STEP 10
Continue this process until the remaining amount is0. The prizes are 256, 64, 8, $4.
STEP 11
Count the number of prizes to find the minimum number of prizes that could be distributed.
The minimum number of prizes that could be distributed from $988 is7.
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