Arnold started getting an allowance at his tenth birthday. Each month he got three times as many dollars as he was years old. If he saved 25% of his allowance, how much money would he
have saved by the day before his 18th birthday?
I got 972 but the way I did it was too complicated and long, I was wondering if you can help me solve it in a quicker way
Look at my solution for the earlier one where he got dollars equal to year
You get an arithmetic series in there which simplifies the sum a bit.
Oh! In fact this problem is just the earlier one times 3
3 * 324 = 972
Sure! I can help you solve it step-by-step. Let's break it down.
1. We know that Arnold started getting an allowance at his tenth birthday, which means he received an allowance for 8 years before his 18th birthday.
2. Each month, Arnold got three times as many dollars as he was years old. So, at his 10th birthday, he received 10 * 3 = 30 dollars.
3. We need to calculate how much money he received each month for 8 years. Since there are 12 months in a year, we multiply 8 years by 12 months to get 8 * 12 = 96 months.
4. We can then multiply the number of months by the monthly allowance to find the total amount of money he received over 8 years. 96 months * 30 dollars/month = 2880 dollars.
5. Next, we need to find out how much money Arnold saved. We are told that he saved 25% of his allowance. To calculate this, we can multiply the total amount of money he received by 25% or 0.25. 2880 dollars * 0.25 = 720 dollars.
So, Arnold would have saved a total of 720 dollars by the day before his 18th birthday.
Sure, I can help you solve this problem more quickly. Let's break it down step by step:
Step 1: Determine Arnold's age when he started getting an allowance.
Since he started getting an allowance at his tenth birthday, his age at that time is 10 years.
Step 2: Calculate how much allowance he received each month.
Arnold received three times as many dollars as he was years old. So, for each month:
Allowance = 3 * Age
Step 3: Find out how much money Arnold saved each month.
Arnold saved 25% of his allowance. So, the amount he saved each month is:
Saving = 0.25 * Allowance
Step 4: Calculate the total amount Arnold saved by the day before his 18th birthday.
To calculate the total amount, we need to sum up the savings for each month from Arnold's tenth birthday to the day before his 18th birthday (which is when he is 17 years old). Let's go month by month:
Month 1: Arnold is 10 years old.
Allowance = 3 * 10 = 30 dollars
Saving = 0.25 * 30 = 7.5 dollars
Month 2: Arnold is 11 years old.
Allowance = 3 * 11 = 33 dollars
Saving = 0.25 * 33 = 8.25 dollars
Continue this pattern until Arnold is 17 years old, calculating the allowance and savings for each month.
Once you have the savings for each month, sum them up to get the total savings amount.
I hope this explanation helps you solve the problem more quickly and efficiently.