I'm saving money over a year to buy a $157.50 gift. I start with an empty piggybank. I put in a small amount of money. Each month after January, I put in $1.75 more than I put in the previous month. By the end of the December I've saved $157.50 exactly. The amount of dollars that I had in my piggy bank after April's deposit was...?
To solve this problem, let's break it down step by step:
1. First, let's determine how much money you saved each month. Starting with January, we need to calculate the amount you saved each subsequent month.
January: Let's assume you saved X dollars in January.
February: You saved $1.75 more than January, so you saved (X + $1.75) in February.
March: You saved $1.75 more than February, so you saved ((X + $1.75) + $1.75) = (X + $3.50) in March.
April: Following the same pattern, you saved ((X + $3.50) + $1.75) = (X + $5.25) in April.
2. Since we want to find out the amount of money you had in your piggy bank after April's deposit, we need to sum up the savings from January to April.
Total savings from January to April = (X + (X + $1.75) + (X + $3.50) + (X + $5.25))
3. According to the problem, the total savings by the end of December is $157.50. So we can set up the equation:
Total savings from January to April = $157.50
(X + X + $1.75 + X + $3.50 + X + $5.25) = $157.50
4. Simplify the equation:
(4X + $10.50) = $157.50
5. Subtract $10.50 from both sides:
4X = $147.00
6. Divide both sides by 4 to isolate X:
X = $36.75
Therefore, you saved $36.75 in January.
7. Finally, to find out the amount of dollars you had in your piggy bank after April's deposit, substitute X into the expression for April's savings:
April's savings = (X + $5.25) = ($36.75 + $5.25) = $42.00
So, after April's deposit, you had $42.00 in your piggy bank.
You have an AP with
a = ?
d = 1.75
S12 = 12/2 (2a + 11*1.75) = 157.50
Now just solve for 3.50
In April,
S4 = 5/2 (2a = 4d)