Kristen is considering hiring a moving company. Sanford's Plus charges an initial fee of $125 plus $165 per hour? Quality moving Company charges an initial fee of $200 plus $145 per hour.

Question

If either company were hired for (blank) hours, the total cost would be the same.
If Sanford's Plus is hired for 12 hours, it would cost how much?

Answer 1

To find out how many hours it would take for the total cost of both moving companies to be the same, we can set up an equation based on their pricing structures.

Let \( h \) be the number of hours.

The total cost for Sanford's Plus can be expressed as: \[ \text{Cost}_{\text{Sanford's Plus}} = 125 + 165h \]

The total cost for Quality Moving Company can be expressed as: \[ \text{Cost}_{\text{Quality Moving}} = 200 + 145h \]

To find out when these costs are the same, we can set the two equations equal to each other: \[ 125 + 165h = 200 + 145h \]

Now, we can solve for \( h \):

1. Subtract \( 145h \) from both sides: \[ 125 + 165h - 145h = 200 \] \[ 125 + 20h = 200 \]

2. Subtract 125 from both sides: \[ 20h = 200 - 125 \] \[ 20h = 75 \]

3. Divide by 20: \[ h = \frac{75}{20} \] \[ h = 3.75 \]

So, if either company were hired for 3.75 hours, the total cost would be the same.

Next, we need to calculate how much it would cost if Sanford's Plus is hired for 12 hours: \[ \text{Cost}_{\text{Sanford's Plus}} = 125 + 165 \times 12 \]

Calculating this:

1. Multiply \( 165 \) by \( 12 \): \[ 165 \times 12 = 1980 \]

2. Add the initial fee: \[ 125 + 1980 = 2105 \]

Therefore, if Sanford's Plus is hired for 12 hours, it would cost $2,105.