Questions: Write and solve each equation.
1. Pedro opened his account with 710 and withdrew 35 per week. Maria opened her account with 570 and withdrew 25 weekly. In how many weeks will their accounts be equal.
Transcript text: Write and solve each equation.
1. Pedro opened his account with $\$ 710$ and withdrew $\$ 35$ per week. Maria opened her account with $\$ 570$ and withdrew $\$ 25$ weekly. In how many weeks will their accounts be equal.
Solution
Solution Steps
To find out in how many weeks Pedro's and Maria's accounts will be equal, we need to set up an equation where the remaining balance in both accounts is the same. Pedro's account balance can be represented as 710−35w and Maria's as 570−25w, where w is the number of weeks. We solve the equation 710−35w=570−25w to find the value of w.
Step 1: Set Up the Equations
We define the account balances for Pedro and Maria after w weeks. Pedro's balance is given by:
P(w)=710−35w
Maria's balance is given by:
M(w)=570−25w
Step 2: Set the Equations Equal
To find when their accounts are equal, we set the two equations equal to each other:
710−35w=570−25w
Step 3: Solve for w
Rearranging the equation, we combine like terms:
710−570=35w−25w
This simplifies to:
140=10w
Dividing both sides by 10 gives:
w=14
Final Answer
The accounts will be equal after w=14 weeks. Thus, the final answer is:
w=14