Jack needs to hire someone to feed and walk his dogs while he is away on a business trip. His neighbor said that she can do it for $\$40$ per day. He also found a pet-sitting company that charges $\$25$ per day, plus a $\$75$ registration fee. $\newline$ Which equation can you use to find $d$ , the number of days the trip would need to last for the two options to cost the same? $\newline$ Choices: $\newline$ (A) $40d + 25 = 75d$ $\newline$ (B) $40d = 25d + 75$ $\newline$ How many days would the trip need to last for the two options to cost the same? $\newline$ $\_\_\_$ days $\newline$

Full solution

Q. Jack needs to hire someone to feed and walk his dogs while he is away on a business trip. His neighbor said that she can do it for

\$40

per day. He also found a pet-sitting company that charges

\$25

per day, plus a

\$75

registration fee.

\newline

Which equation can you use to find

d

, the number of days the trip would need to last for the two options to cost the same?

\newline

Choices:

\newline

(A)

40d + 25 = 75d

\newline

(B)

40d = 25d + 75

\newline

How many days would the trip need to last for the two options to cost the same?

\newline

\_\_\_

days

\newline

Set up equation: First, let's set up the equation to find when both options cost the same. The neighbor charges $\$40$ per day, so for $d$ days, it's $40d$ dollars. The pet-sitting company charges $\$25$ per day plus a $\$75$ registration fee, so for $d$ days, it's $25d + 75$ dollars. Set these equal to find $d$ : $40d = 25d + 75$ .
Isolate terms with $d$ : Now, solve for $d$ . Subtract $25d$ from both sides to isolate the terms with $d$ on one side: $40d - 25d = 75$ .
Simplify equation: Simplify the equation: $15d = 75$ .
Divide to solve for d: Divide both sides by $15$ to solve for $d$ : $d = \frac{75}{15}$ .
Calculate d: Calculate $d$ : $75$ divided by $15$ equals $5$ . So, $d = 5$ .