Question

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