QuestionWhat is the minimum number of prizes, all powers of 2, that can total \$820?
Studdy Solution
STEP 1
Assumptions1. The total prize money is $820. The prizes are distributed in powers of3. We need to find the minimum number of prizes
STEP 2
First, we need to understand what powers of2 are. Powers of2 are numbers that result from raising2 to various exponents. They are1,2,4,8,16,32,64,128,256,512,1024, and so on.
STEP 3
To minimize the number of prizes, we should start by distributing the largest possible power of2 that is less than or equal to the total prize money.
STEP 4
The largest power of2 less than or equal to 512.
STEP 5
Subtract the value of the largest power of2 from the total prize money.
STEP 6
Plug in the values for the total prize money and the largest power of2 to calculate the remaining money.
STEP 7
Calculate the remaining money.
STEP 8
Repeat the process of distributing the largest possible power of2 that is less than or equal to the remaining money.
STEP 9
The largest power of2 less than or equal to 256.
STEP 10
Subtract the value of the largest power of2 from the remaining money.
STEP 11
Plug in the values for the remaining money and the largest power of to calculate the new remaining money.
STEP 12
Calculate the new remaining money.
STEP 13
Continue the process until all the money is distributed.
STEP 14
The largest power of2 less than or equal to 32.
STEP 15
Subtract the value of the largest power of2 from the remaining money.
STEP 16
Plug in the values for the remaining money and the largest power of2 to calculate the new remaining money.
STEP 17
Calculate the new remaining money.
STEP 18
The largest power of2 less than or equal to 16.
STEP 19
Subtract the value of the largest power of from the remaining money.
STEP 20
Plug in the values for the remaining money and the largest power of to calculate the new remaining money.
STEP 21
Calculate the new remaining money.
STEP 22
The largest power of less than or equal to 4.
STEP 23
Subtract the value of the largest power of from the remaining money.
STEP 24
Plug in the values for the remaining money and the largest power of to calculate the new remaining money.
STEP 25
Calculate the new remaining money.
STEP 26
Now that all the money is distributed, count the number of prizes.
The prizes are 256, 16, and $4.
The minimum number of prizes that could be distributed from $820 is5.
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