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.
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Solution

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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 71035w710 - 35w and Maria's as 57025w570 - 25w, where ww is the number of weeks. We solve the equation 71035w=57025w710 - 35w = 570 - 25w to find the value of ww.

Step 1: Set Up the Equations

We define the account balances for Pedro and Maria after w w weeks. Pedro's balance is given by: P(w)=71035w P(w) = 710 - 35w Maria's balance is given by: M(w)=57025w 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: 71035w=57025w 710 - 35w = 570 - 25w

Step 3: Solve for w w

Rearranging the equation, we combine like terms: 710570=35w25w 710 - 570 = 35w - 25w This simplifies to: 140=10w 140 = 10w Dividing both sides by 10 gives: w=14 w = 14

Final Answer

The accounts will be equal after w=14 w = 14 weeks. Thus, the final answer is: w=14 \boxed{w = 14}

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