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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\$40 per day. He also found a pet-sitting company that charges $25\$25 per day, plus a $75\$75 registration fee.\newlineWhich equation can you use to find dd, the number of days the trip would need to last for the two options to cost the same?\newlineChoices:\newline(A) 40d=25d+7540d = 25d + 75\newline(B) 40d+25=75d40d + 25 = 75d\newlineHow many days would the trip need to last for the two options to cost the same?\newline___\_\_\_ days\newline

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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\$40 per day. He also found a pet-sitting company that charges $25\$25 per day, plus a $75\$75 registration fee.\newlineWhich equation can you use to find dd, the number of days the trip would need to last for the two options to cost the same?\newlineChoices:\newline(A) 40d=25d+7540d = 25d + 75\newline(B) 40d+25=75d40d + 25 = 75d\newlineHow many days would the trip need to last for the two options to cost the same?\newline___\_\_\_ days\newline
  1. Set Total Cost Equation: To find the equation that represents the point at which both options cost the same, we need to set the total cost of the neighbor's service equal to the total cost of the pet-sitting company's service.\newlineNeighbor's service cost: $40\$40 per day for dd days is represented as 40d40d.\newlinePet-sitting company's service cost: $25\$25 per day for dd days plus a $75\$75 registration fee is represented as 25d+7525d + 75.\newlineThe equation that equates these two costs is 40d=25d+7540d = 25d + 75.
  2. Solve for Variable: Now we need to solve the equation 40d=25d+7540d = 25d + 75 for dd to find out after how many days the costs will be the same.\newlineFirst, subtract 25d25d from both sides to isolate the variable dd on one side of the equation.\newline40d25d=25d+7525d40d - 25d = 25d + 75 - 25d\newlineThis simplifies to 15d=7515d = 75.
  3. Find Number of Days: Next, divide both sides of the equation by 1515 to solve for dd. \newline15d15=7515\frac{15d}{15} = \frac{75}{15}\newlineThis simplifies to d=5d = 5.

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