Solve the following real-world problem: Destiny opens a checking account with $100 and then deposits $27 each week. How many weeks will it take her account to reach $343?
To solve this problem, we need to find the number of weeks it will take Destiny's account to reach $343.
We start with an initial amount of $100 in her account and each week she deposits an additional $27.
Let's create an equation to represent this situation:
100 + 27w = 343
Here, w represents the number of weeks it will take her account to reach $343.
To solve for w, we can subtract 100 from both sides of the equation:
27w = 343 - 100
27w = 243
Finally, divide both sides of the equation by 27 to solve for w:
w = 243 /27
w = 9
Therefore, it will take Destiny's account 9 weeks to reach $343.
To solve this real-world problem, we need to determine the number of weeks it will take for Destiny's account balance to reach $343. We know that Destiny starts with $100 in her account and deposits $27 each week.
A simple way to solve this problem is to set up an equation to represent the situation. Let's use the variable 'w' to represent the number of weeks it takes for the account balance to reach $343.
The initial account balance is $100, and Destiny deposits $27 each week. So, the equation can be written as:
100 + 27w = 343
To find the value of 'w', we need to isolate the variable. We can do this by subtracting 100 from both sides of the equation:
27w = 343 - 100
27w = 243
Dividing both sides of the equation by 27:
w = 243 / 27
Simplifying this expression, we get:
w = 9
Therefore, it will take Destiny 9 weeks for her account balance to reach $343.
In summary, to solve this real-world problem, we set up an equation using the initial account balance, the weekly deposit, and the desired account balance. Then we solved the equation to find the number of weeks needed.
To find out how many weeks it will take Destiny's account to reach $343, we can use the formula for arithmetic sequences.
The first term, a = $100
The common difference, d = $27
Let's assume it takes n weeks to reach $343.
The formula for the nth term of an arithmetic sequence is:
an = a + (n-1)d
Substituting the given values into the formula, we have:
343 = 100 + (n-1)27
Simplifying the equation:
343 = 100 + 27n - 27
343 - 100 = 27n - 27
243 = 27n - 27
To isolate n, we can add 27 to both sides:
243 + 27 = 27n
270 = 27n
Now, we can solve for n by dividing both sides by 27:
270/27 = n
10 = n
Therefore, it will take Destiny's account 10 weeks to reach $343.