Solve the following real world problem. Destiny opens a checking account with $109 and then deposits $27 each week. How many weeks will it take for her account to reach $343?
It will take Destiny 12 weeks to reach $343.
To solve this problem, we need to determine the number of weeks it will take for Destiny's account balance to reach $343.
Let's break it down step by step:
1. Define the initial balance: Destiny opens the checking account with $109.
2. Determine the amount deposited each week: Destiny deposits $27 each week.
3. Calculate the increase in the account balance each week: Since Destiny deposits $27 every week, her account balance increases by $27 every week.
4. Set up an equation: We need to find the number of weeks (let's call it "x") it will take for the account balance to reach $343. We can represent this situation with the equation:
Initial balance + (Increase per week) * (Number of weeks) = Desired balance
$109 + $27x = $343
5. Solve the equation for x: We can solve for x by isolating it on one side of the equation.
$109 + $27x = $343
Subtract $109 from both sides of the equation:
$27x = $343 - $109
$27x = $234
Divide both sides of the equation by $27 to isolate x:
x = $234 ÷ $27
6. Calculate the value of x: Perform the division.
x ≈ 8.67
Since x represents the number of weeks, we round up to the nearest whole number.
Therefore, it will take approximately 9 weeks for Destiny's account to reach $343.
To solve this problem step by step, we can set up an equation.
Let's assume that the number of weeks it takes for Destiny's account to reach $343 is represented by 'w'.
The initial amount in her account is $109, and she deposits $27 each week. Thus, the amount in her account after 'w' weeks can be represented as:
Amount = Initial amount + (Deposit per week × Number of weeks)
Amount = $109 + ($27 × w)
We know that the amount should reach $343, so we can now set up an equation:
$343 = $109 + ($27 × w)
To solve for 'w', we can isolate the variable 'w' on one side of the equation:
$343 - $109 = $27 × w
$234 = $27 × w
Finally, we can solve for 'w' by dividing both sides of the equation by $27:
w = $234 ÷ $27
Now, calculating this value gives us:
w = 8.6666...
Since we can't have a fraction of a week, we round up to the nearest whole number.
Therefore, it will take approximately 9 weeks for Destiny's account to reach $343.