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.

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: \[ w = 14 \]