You are planning on installing a security system at your home. For Safety First Security, you can get monitoring for $2

Question

a day with a one-time set-up fee of $150
. For Home Safety Security, you can get monitoring for $1.50
a day with a one-time set-up fee of $200
. Using substitution, find the number of days for which both companies would cost the same.

Answer 1

To find the number of days for which both companies would cost the same, we can set up equations based on the given information.

Let \( x \) be the number of days.

For Safety First Security:

• Cost = Setup fee + Daily monitoring cost
• Cost = \( 150 + 2x \)

For Home Safety Security:

• Cost = Setup fee + Daily monitoring cost
• Cost = \( 200 + 1.5x \)

We set the two costs equal to find \( x \): \[ 150 + 2x = 200 + 1.5x \]

Now, we can solve for \( x \).

1. Subtract \( 1.5x \) from both sides: \[ 150 + 2x - 1.5x = 200 \] \[ 150 + 0.5x = 200 \]

2. Subtract 150 from both sides: \[ 0.5x = 200 - 150 \] \[ 0.5x = 50 \]

3. Multiply both sides by 2 to solve for \( x \): \[ x = 100 \]

Thus, both companies would cost the same after 100 days.