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: $\newline$ $(A) 9d - 25 = 920$ $\newline$ $(B) 9(d - 25) = 920$ $\newline$ $(C) 25d - 9 = 920$ $\newline$ $(D) 25(d - 9) = 920$ $\newline$ How much does the agency charge per day? $\newline$ ____ $\$$

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Grade 7

Solve 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) 9d - 25 = 920

\newline

(B) 9(d - 25) = 920

\newline

(C) 25d - 9 = 920

\newline

(D) 25(d - 9) = 920

\newline

How much does the agency charge per day?

\newline

____

\$

Understand the problem: Understand the problem. $\newline$ The Logan family is renting a beach house for $9$ days with a one-time discount of $\$25$ . The total cost is $\$920$ . We need to find the daily rental charge, which is represented by $d$ .
Set up the equation: Set up the equation. $\newline$ The total cost without the discount would be $9$ days times the daily rate $(9d)$ . Since there is a one-time discount of $\$25$ , we subtract that amount from the total cost to get the equation that represents the situation: $9d - 25 = 920$ .
Identify the correct equation: Identify the correct equation from the choices. $\newline$ Looking at the choices given, we can see that option (A) $9d - 25 = 920$ matches the equation we set up in Step $2$ . Therefore, the correct equation to use is: $\newline$ (A) $9d - 25 = 920$
Solve the equation for d: Solve the equation for d. $\newline$ To find the daily rental charge, we need to solve the equation for d: $\newline$ $9d - 25 = 920$ $\newline$ First, add $25$ to both sides of the equation to isolate the term with $d$ : $\newline$ $9d - 25 + 25 = 920 + 25$ $\newline$ $9d = 945$ $\newline$ Next, divide both sides by $9$ to solve for $d$ : $\newline$ $\frac{9d}{9} = \frac{945}{9}$ $\newline$ $d = 105$