you finally have your holiday shopping money! you put $2 away in January, $4 away in February, $8 away in March, $16 away in April and followed this savings pattern through to Decemberf, How much money do you have to shop with?
It's tricky for me 'coz I interpreted the above in 2 different ways. My answer is $4096 and my other answer is $90
Please help. Thanks
2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1024 + 2048 + 4096 = ? Looks like you have even more than 4096.
yes, my answer of $4096 is only for December savings, so the total for Jan to Dec is $8190.
Thank you so much Ms Sue. Happy Holidays!!
You're very welcome. Happy holidays to you, too.
To solve this problem, we need to determine the total amount of money saved over the course of the year by following the given savings pattern.
One way to interpret the savings pattern is that in each successive month, you save double the amount from the previous month. Another way to interpret it is that each month, you save an amount equal to the sum of all the previous months' savings plus the amount saved in that particular month.
Let's calculate the total savings using both interpretations:
1. Calculating using the doubling savings pattern:
If we follow the doubling savings pattern, the savings sequence would be as follows:
January: $2
February: $4
March: $8
April: $16
May: $32
June: $64
July: $128
August: $256
September: $512
October: $1024
November: $2048
December: $4096
Therefore, using the doubling savings pattern, you would have $4,096 to shop with.
2. Calculating using the cumulative savings pattern:
If we follow the cumulative savings pattern, the savings sequence would be as follows:
January: $2
February: $2 + $4 = $6
March: $2 + $4 + $8 = $14
April: $2 + $4 + $8 + $16 = $30
May: $2 + $4 + $8 + $16 + $32 = $62
June: $2 + $4 + $8 + $16 + $32 + $64 = $126
July: $2 + $4 + $8 + $16 + $32 + $64 + $128 = $254
August: $2 + $4 + $8 + $16 + $32 + $64 + $128 + $256 = $510
September: $2 + $4 + $8 + $16 + $32 + $64 + $128 + $256 + $512 = $1022
October: $2 + $4 + $8 + $16 + $32 + $64 + $128 + $256 + $512 + $1024 = $2046
November: $2 + $4 + $8 + $16 + $32 + $64 + $128 + $256 + $512 + $1024 + $2048 = $4094
December: $2 + $4 + $8 + $16 + $32 + $64 + $128 + $256 + $512 + $1024 + $2048 + $4096 = $8190
Therefore, using the cumulative savings pattern, you would have $8,190 to shop with.
Based on the two possible interpretations of the savings pattern, the two potential answers are $4,096 and $8,190.