Sove the following real-world problem: Destiny opens a checking account with $200 and then deposits $27 each week. How many weeks will it take her account to reach $343?
To solve this problem, we can set up an equation. Let's represent the number of weeks as "w".
Given that Destiny deposits $27 each week, the total amount in her account after w weeks would be 200 + 27w.
We want to find the number of weeks it takes for the account to reach $343, so we can set up the following equation:
200 + 27w = 343
To isolate the variable, we can subtract 200 from both sides:
27w = 343 - 200
27w = 143
Finally, we can solve for w by dividing both sides by 27:
w = 143/27
w ≈ 5.296
Since we cannot have a fraction of a week, we need to round up to the nearest whole number.
It will take Destiny approximately 6 weeks for her account to reach $343.
To solve this problem, we need to determine the number of weeks it will take for Destiny's account to reach $343 starting from an initial balance of $200 and a weekly deposit of $27.
1. Initialize a variable to keep track of the current account balance. Let's call it "balance" and set it to $200.
balance = $200
2. Initialize a counter variable to keep track of the number of weeks. Let's call it "weeks" and set it to 0.
weeks = 0
3. Repeat the following steps until the balance reaches $343:
a. Add the weekly deposit of $27 to the current balance.
balance = balance + $27
b. Increment the number of weeks by 1.
weeks = weeks + 1
4. Once the balance reaches $343, stop the loop and output the number of weeks it took.
Output: It will take Destiny "weeks" weeks to reach an account balance of $343.
Let's compute the values step-by-step:
Week 1:
balance = $200 + $27 = $227
(balance is still less than $343, continue)
Week 2:
balance = $227 + $27 = $254
(balance is still less than $343, continue)
Week 3:
balance = $254 + $27 = $281
(balance is still less than $343, continue)
Week 4:
balance = $281 + $27 = $308
(balance is still less than $343, continue)
Week 5:
balance = $308 + $27 = $335
(balance is still less than $343, continue)
Week 6:
balance = $335 + $27 = $362
(balance is greater than $343, stop)
Output: It will take Destiny 6 weeks to reach an account balance of $343.
To solve this problem, we need to determine how many weeks it will take for Destiny's account to reach $343.
Let's break down the information we have:
- Destiny opens the checking account with an initial balance of $200.
- She deposits $27 each week.
We can set up an equation to represent this situation:
Account balance after n weeks = Initial balance + (Weekly deposit * Number of weeks)
Using this equation, we can solve for the number of weeks needed to reach $343.
Account balance after n weeks = $200 + ($27 * n)
Now let's set up the equation based on the given information and solve for n:
$200 + ($27 * n) = $343
To solve for n, we first need to isolate the variable on one side of the equation.
Subtract $200 from both sides:
$27 * n = $343 - $200
$27 * n = $143
Next, divide both sides of the equation by $27 to solve for n:
n = $143 / $27
n ≈ 5.296
Since we cannot have a fraction of a week, we round up the answer to the nearest whole number.
Therefore, it will take approximately 6 weeks for Destiny's account to reach $343.