Can you help me with this problem?
At the beginning of January, Lisa had some money in her savings account. Each month she was able to deposit enough from her allowance to double the amount currently in the account. However, she had a loan to pay off, requiring her to withdraw $10 from the account monthly. At the end of May, she had $2 left in the account. How much did Lisa have at the beginning of January?
At the beginning of January, Lisa had some money in her savings account. Each month she was able to deposit enough from her allowance to double the amount currently in the account. However, she had a loan to pay off, requiring her to withdraw $10 from the account monthly. At the end of May, she had $2 left in the account. How much did Lisa have at the beginning of January?
It depends on when the money was doubled, before or after the $10.00 was paid out.
One way:
Jan.1--$X
Feb.1--$2X - 10
Mar.1--$(4X - 20) - 10 = (4X - 30)
Apr.1--$(8X - 60) - 10 = (8X - 70)
May 1--$(16X - 140) - 10 = (16X - 150)
16X - 150 = 2 or X = $9.50
The other way:
Jan.1--$X
Feb.1--$(X - 10)2
Mar.1--$[(X - 10)2 - 10]2
Apr.1--I'll let you finish this one.
Jan.1st $X
Feb.1st 2X - 10
Mar.1st
thanks
Sure, I can help you with that problem!
We can solve this problem by working backwards and calculating how much money Lisa had in her account at the end of each month.
Let's start with the end of May, when Lisa had $2 left in her account. We know that she had to withdraw $10 every month to pay off her loan. So we can subtract $10 from $2 to find out how much money she had at the end of April.
$2 - $10 = -$8
Since we can't have negative money, this means Lisa didn't have any money left in her account at the end of April. So now let's figure out how much money she had at the end of March.
To do this, we'll use the fact that each month she was able to deposit enough from her allowance to double the amount currently in the account. Let's call the amount of money Lisa had at the end of March "x". Since Lisa doubled her money each month, she must have had half that amount at the end of February.
So at the end of February, Lisa had x/2 dollars. From this, we can calculate how much money she had at the end of March by doubling x/2.
2 * (x/2) = x
So at the end of March, Lisa had x dollars.
Now, we know that she had to withdraw $10 each month. So her account balance at the end of March must have been $10 higher than her balance at the end of February, which was x/2.
x/2 + $10 = x
Now, let's solve this equation to find the value of x.
To do this, we'll multiply both sides of the equation by 2 to get rid of the fraction:
2 * (x/2 + $10) = 2 * x
Simplifying the equation:
x + $20 = 2x
Subtracting x from both sides:
$20 = x
So, Lisa had $20 in her account at the beginning of January.
Therefore, Lisa had $20 at the beginning of January.