Question

First safety for $2 per day plus a $150 set up fee
Safety security for $1.50 per day plus $200 set up fee
On what day would both companies cost the same

Answer 1

To find the day when both companies cost the same, we can set up equations representing the total cost of each service over a certain number of days.

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

1. For the first company, the total cost \( C_1 \) is given by:
\[
C_1 = 150 + 2x
\]
where \( 150 \) is the setup fee and \( 2x \) is the cost per day.

2. For the second company, the total cost \( C_2 \) is given by:
\[
C_2 = 200 + 1.5x
\]
where \( 200 \) is the setup fee and \( 1.5x \) is the cost per day.

To find out when the costs are the same, we can set the equations equal to each other:
\[
150 + 2x = 200 + 1.5x
\]

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

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

2. Subtract \( 150 \) from both sides:
\[
0.5x = 50
\]

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

Thus, both companies will cost the same after **100 days**.