Questions: 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. 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? 40d=25d+75 How many days would the trip need to last for the two options to cost the same? days

Solution Steps

To find the number of days \( d \) for which the cost of hiring the neighbor and the pet-sitting company are the same, we need to set up an equation where the total cost for both options is equal. The neighbor charges $40 per day, so the cost is \( 40d \). The pet-sitting company charges $25 per day plus a $75 registration fee, so the cost is \( 25d + 75 \). We set these two expressions equal to each other and solve for \( d \).

To find the number of days \( d \) for which the costs of hiring the neighbor and the pet-sitting company are equal, we set up the equation based on their costs: \[ 40d = 25d + 75 \]

We can simplify the equation by isolating \( d \): \[ 40d - 25d = 75 \] This simplifies to: \[ 15d = 75 \] Dividing both sides by 15 gives: \[ d = 5 \]

Final Answer