Dominic's Spending: How Much Did He Start With?

Hey guys! Let's dive into a fun little math problem. We're going to help Dominic figure out how much money he had on Sunday, based on his spending habits throughout the week. It's like being a financial detective, piecing together clues to uncover the mystery of his starting balance. This is a great exercise in tracking finances, and it's something everyone can benefit from. Let's break down Dominic's spending pattern and use our math skills to solve this puzzle. Ready to get started? Let's go!

Decoding Dominic's Spending: The Weekly Breakdown

Okay, so the first thing we need to do is get a clear picture of Dominic's spending. We have a table that shows his debits (money he spent) and credits (money he received or added) each day. This is the key to unlocking the answer. Remember, debits decrease his money, and credits increase his money. It's like the basic principle of a bank account! Think of it like this: every time he spends money, the balance goes down, and every time he gets money, the balance goes up. To get a better grasp, let's look at the table you provided. This breakdown is crucial for calculating Dominic's starting amount. We'll be using this data to work backward, day by day, to find out how much he had on Sunday. This approach will allow us to accurately calculate his Sunday balance.

Now, let's take a look at the table you've presented to get started on the process. Here's a look at the data:

With this information, we can calculate how much money he had at the start of each day. We'll start from the end of the week and work backward, which is the most effective approach for this problem. We'll also use this data to perform some calculations, so get ready to use your math skills! It's all about adding and subtracting to track his money flow. This meticulous approach ensures accuracy, and we'll break it down step by step to keep things easy to follow. Each day represents a step in our journey to find the amount he had on Sunday. Remember, the goal is to understand how Dominic's money changed over the week, so it’s essential to be thorough.

Working Backwards: Unveiling Sunday's Balance

Alright, buckle up, because we're about to do some reverse engineering! We know how Dominic spent and received money throughout the week, but we need to figure out his starting point. This means we'll begin with the information we have and work backward to Sunday. Think of it as a financial time machine, taking us back to the beginning of the week. Remember, each day's balance is affected by the debits (money spent) and credits (money received). Let's start with Saturday since it is before Sunday. Saturday is the last day we have direct info about before Sunday. On Saturday, Dominic received $100, which means that before receiving this money, he had $100 less. Since we don't know the exact starting amount on Sunday, we'll assign a variable to represent it. Let's call it 'S'. This variable will help us track the changes in his money as we move through the days. This is where it gets really fun! We'll use the information from the table and the variable to build our equations. It's like solving a puzzle, and each step brings us closer to the solution. The core idea is to find out the amount of money Dominic had on Sunday. Keep in mind that his spending and receiving money will change the amount of the cash in his bank.

Let's keep going! Let's say Dominic started with 'S' dollars on Sunday. On Saturday, he received $100. So, to find out how much he had at the start of Saturday, we'd subtract the $100 he received from the Sunday amount (S). Then, on Friday, he spent $62. That means, before the spending, he had an extra $62. On Thursday, he received $50. Before receiving this amount, he had $50 less. Continuing this pattern, we will go through Wednesday, Tuesday, and Monday. Now we have everything we need to find out how much he had on Sunday. By tracking the transactions day by day, we can create the steps. Let’s do the calculation!

The Calculation: Sunday's Fund Uncovered

Okay, guys, it's time to crunch some numbers! We've got all the pieces of the puzzle, and now we need to put them together. We'll start from the last known value, work backward through the week, and calculate Dominic's starting balance. This is where all the groundwork we've laid pays off! Remember, the goal is to work backward, adjusting for each debit and credit to find that initial Sunday amount. Each day's balance is a result of the debits and credits from that day. We're going to keep it simple, one step at a time, to avoid any confusion. So, let's start with Saturday, the last day we have solid data. We know that on Saturday, he received $100. To find out what he had at the start of Saturday, we have to consider all the transactions that happened that day. Now, let’s go through each day, step by step:

• Saturday: Dominic received $100.
• Friday: Dominic spent $62.
• Thursday: Dominic received $50.
• Wednesday: Dominic spent $75.
• Tuesday: Dominic received $200.
• Monday: Dominic spent $158.

Here’s how we can find out the amount of money he had on Sunday, using variables:

• Let 'S' be the amount Dominic had on Sunday.
• On Monday, he spent $158. Before this spending, he had S + 158.
• On Tuesday, he received $200. Before receiving this amount, he had S + 158 - 200.
• On Wednesday, he spent $75. Before this spending, he had S + 158 - 200 + 75.
• On Thursday, he received $50. Before receiving this amount, he had S + 158 - 200 + 75 - 50.
• On Friday, he spent $62. Before this spending, he had S + 158 - 200 + 75 - 50 + 62.
• On Saturday, he received $100. Before receiving this amount, he had S + 158 - 200 + 75 - 50 + 62 - 100.

Now, if we suppose that he spent nothing and received nothing on Sunday, then all these operations above are exactly equal to the amount of money on Sunday. Simplifying this, we get: S = S + 158 - 200 + 75 - 50 + 62 - 100. Now we calculate this: S = S + 158 - 200 + 75 - 50 + 62 - 100 = S - 5. To be clear, for the calculation, the result is: S = S - 5. This result implies that the balance must have increased by 5. Therefore, the balance on Sunday was $5.

Conclusion: The Final Verdict

Awesome, we did it! We successfully navigated Dominic's spending patterns and determined how much money he had on Sunday. It was a journey through debits and credits, a bit of backward calculation, and a whole lot of fun. We broke down each day's transactions and used them to solve this problem. The final amount of money Dominic had on Sunday was $5.

So, guys, what did we learn? We learned how to track and analyze spending, and we learned how to work backward to solve a financial problem. It shows how important it is to track your money, so you know where it is going. It's an excellent method for understanding where your money is going and where it's coming from. Keep in mind that managing money starts with understanding where it goes! Until next time, keep those financial detective skills sharp. And always remember to track your spending. This simple habit can go a long way in helping you manage your money wisely. Goodbye! And thank you for joining me on this fun journey!