Please help me write the equation that goes with the following word problem and solve it using invert operations.

Question

Your piggy banks starts off with 3 dollars,each day you put 2 dollars on it. After a certain amount of days, there are 19 dollars in your piggy bank. Which of the following equations represents the day,d, when there are 19 dollars in your piggy bank?

Answer 1

For any word problem, consider what each part of the problem means and how the parts relate to each other. Let's the variable 'd' stand for how many days have passed. So when you start, it is day zero and d = 0. In 40 days, d = 40. The other thing that changes is the amount of money in your bank. I don't see a variable in the problem, so let's call it 'm' for money. Like the problem says, your bank starts off with 3 dollars. So at the start (d = 0), m = 3. Then every day, you add two dollars to the bank; the amount of money in the bank (m) increases by 2. How do you represent this mathematically?

Let's try adding "+ 2" to the starting amount to get m = 3 + 2 = 5. So after day 1 (d = 1), m = 5. After day 2 (d = 2), m = 7. After day 3 (d = 3), m = 9. Every day, the amount m increases by (adds) 2. In three days, the amount m increases by 2 * 3. Every d days, the amount m increases by 2 * d. So every d days, we change m = 3 by adding 2d. Thus, we can represent the money in the bank with the formula m = 3 + 2d for d days. Try testing a few values to check that this equation works.

To find the equation where there are 19 dollars in your piggy bank, remember that m is the number of dollars in your piggy bank. What is the value of m in this situation? Use the previous equation to help.

Now that you have an equation, you should be able to solve it by inverting some operations. Remember that when doing this, you should add or subtract BEFORE you multiply or divide. Hope this helps you start the problem!