Hey there! Let's answer each part of this question in order.
Part a
If Pedro withdrew [tex]\$35[/tex] per week, his change in balance could be represented as [tex]-35x[/tex] since [tex]x[/tex] is the number of weeks. Add this to his initial balance of [tex]\$710[/tex] to get the first answer:
[tex]\huge\boxed{710-35x}[/tex]
Part b
The same concepts can be applied to solve the next part. Maria started off with [tex]\$570[/tex] in her account and withdrew [tex]\$25[/tex] each week. Apply the same process from the first part to get the second answer:
[tex]\huge\boxed{570-25x}[/tex]
Part c
Write an equation
For the last part, we need to find the value of [tex]x[/tex] that makes the expressions we made in the first two parts equal to each other, so start by making them into an equation.
[tex]\huge\boxed{710-35x=570-25x}[/tex]
Solve the equation
Now we need to solve this equation. Start by bringing the constants to the right and the variables to the left.
Keep in mind that when you move a term to the other side of the equation, you need to change its sign, as you are adding or subtracting the same number from both sides of the equation.
[tex]\begin{aligned}710-35x&=570-25x\\-35x&=570-25x-710\\-35x+25x&=570-710\end{aligned}[/tex]
Now, combine the like terms with addition and subtraction.
[tex]\begin{aligned}-35x+25x&=570-710\\-10x&=-140\end{aligned}[/tex]
Finally, divide both sides of the equation by [tex]-10[/tex] to fully isolate the variable and find the final answer.
[tex]\begin{aligned}-10x&=-140\\x&=14\ \text{(weeks)}\end{aligned}[/tex]
[tex]\huge\boxed{14\ \text{weeks}}[/tex]
Check your answer
We can also check our answer by substituting the final answer back into each expression, simplifying, and making sure the answers are equal.
[tex]\begin{array}{l|l}710-35x&570-25x\\710-35*14&570-25*14\\710-490&570-350\\220&220\end{array}[/tex]
Since the expressions are equivalent, we know that Pedro's balance is the same as Maria's balance after [tex]14[/tex] weeks.
