The Logan family is renting a beach house from Aqua Coast Beach Rentals. Mr. Logan called the rental agency ahead of time to get the total cost for $9$ days. The rental agent explained that since the family plans to stay during the off-season, there will be a one-time discount of $25$ $\$$ applied to their rental cost. The Logans will pay $920$ $\$$ in all. $\newline$ Which equation can you use to find $d$ , how much the agency charges per day? $\newline$ Choices: $\newline$ $(A) 9(d - 25) = 920$ $\newline$ $(B) 25(d - 9) = 920$ $\newline$ $(C) 25d - 9 = 920$ $\newline$ $(D) 9d - 25 = 920$ $\newline$ How much does the agency charge per day? $\newline$ ____ $\$$

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Solve one-step and two-step equations: word problems

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Q. The Logan family is renting a beach house from Aqua Coast Beach Rentals. Mr. Logan called the rental agency ahead of time to get the total cost for

9

days. The rental agent explained that since the family plans to stay during the off-season, there will be a one-time discount of

25

\$

applied to their rental cost. The Logans will pay

920

\$

in all.

\newline

Which equation can you use to find

d

, how much the agency charges per day?

\newline

Choices:

\newline

(A) 9(d - 25) = 920

\newline

(B) 25(d - 9) = 920

\newline

(C) 25d - 9 = 920

\newline

(D) 9d - 25 = 920

\newline

How much does the agency charge per day?

\newline

____

\$

Set up equation: Let's denote the daily charge by the agency as $d$ dollars per day. Since the Logan family is getting a one-time discount of $25$ dollars and the total cost for $9$ days is $920$ dollars, we can set up an equation that represents the total cost after the discount is applied. The total cost without the discount for $9$ days would be $9d$ dollars. After applying the discount, the total cost is $9d - 25$ dollars. This amount should equal the total cost that the Logans will pay, which is $920$ dollars. Therefore, the equation that represents this situation is: $\newline$ $9d - 25 = 920$ $\newline$ This corresponds to choice (D).
Solve for d: Now, let's solve the equation for d to find out how much the agency charges per day. $\newline$ $9d - 25 = 920$ $\newline$ First, add $25$ to both sides of the equation to isolate the term with d on one side: $\newline$ $9d - 25 + 25 = 920 + 25$ $\newline$ $9d = 945$ $\newline$ Next, divide both sides by $9$ to solve for d: $\newline$ $\frac{9d}{9} = \frac{945}{9}$ $\newline$ $d = 105$ $\newline$ So, the agency charges $105$ dollars per day.