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

View step-by-step help

Home

Math Problems

Grade 7

Solve two-step equations: word problems

Full solution

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) 25(d - 9) = 920

\newline

(B) 25d - 9 = 920

\newline

(C) 9d - 25 = 920

\newline

(D) 9(d - 25) = 920

\newline

How much does the agency charge per day?

\newline

____

\$

Understand the problem: Understand the problem. $\newline$ The total cost for $9$ days is $\$920$ , after applying a one-time discount of $\$25$ . We need to find the daily 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 from the total cost to get the equation $9d - 25 = 920$ .
Identify the correct equation: Identify the correct equation from the choices. $\newline$ The correct equation that represents the situation is $C$ $9d - 25 = 920$ .
Solve the equation for d: Solve the equation for d. $\newline$ Add $25$ to both sides of the equation to isolate the term with d: $\newline$ $9d - 25 + 25 = 920 + 25$ $\newline$ $9d = 945$ $\newline$ Now, divide both sides by $9$ to solve for d: $\newline$ $\frac{9d}{9} = \frac{945}{9}$ $\newline$ $d = 105$
Check the solution: Check the solution. $\newline$ Multiply the daily charge by $9$ days and subtract the discount to see if it equals the total cost: $\newline$ $9 \times 105 - 25 = 945 - 25 = 920$ $\newline$ This matches the total cost given in the problem, so the solution is correct.