Question

peppy pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. happy hounds charges a flat fee of $21 plus $1 per hour. which equation could you use to see when the two companies would charge the same amount?
15x + 3 = 21x + 1
18x = 22x
3x + 15 + 21x = 1
3x + 15 = x + 21

Explanation:

Step1: Define Cost Functions

Let \( x \) be hours. Peppy Pets: \( 15 + 3x \). Happy Hounds: \( 21 + x \).

Step2: Set Costs Equal

To find when costs are equal, set \( 15 + 3x = 21 + x \). Wait, no—wait, recheck. Wait, Peppy: flat $15 + $3 per hour, so \( 3x + 15 \). Happy: flat $21 + $1 per hour, so \( x + 21 \). Wait, no, the first option: \( 15x + 3 = 21x + 1 \)? No, wait, maybe I misread. Wait, Peppy: $15 flat + $3 per hour: \( 3x + 15 \). Happy: $21 flat + $1 per hour: \( x + 21 \). Wait, the last option is \( 3x + 15 = x + 21 \)? Wait, no, the options: first option \( 15x + 3 = 21x + 1 \) – no, that would be if Peppy was $15 per hour + $3 flat, which is wrong. Wait, maybe the problem says Peppy: flat $15 + $3 per hour (so \( 3x + 15 \)), Happy: flat $21 + $1 per hour (so \( x + 21 \)). Wait, but the first option is \( 15x + 3 = 21x + 1 \) – no, that's reversed. Wait, maybe I misread the problem. Let me re-express:

Peppy Pets: flat fee $15 + $3 per hour: total cost \( C_1 = 15 + 3x \).

Happy Hounds: flat fee $21 + $1 per hour: total cost \( C_2 = 21 + x \).

Set \( C_1 = C_2 \): \( 15 + 3x = 21 + x \). Wait, but the options: let's check each:

1. \( 15x + 3 = 21x + 1 \): No, that's per-hour as 15 and 21, flat as 3 and 1 – wrong.

1. \( 18x = 22x \): No.

1. \( 3x + 15 + 21x = 1 \): No.

1. \( 3x + 15 = x + 21 \): Yes! Wait, \( 3x + 15 \) (Peppy: 3 per hour, 15 flat) and \( x + 21 \) (Happy: 1 per hour, 21 flat). So setting them equal: \( 3x + 15 = x + 21 \). Wait, but let's check the first option again. Wait, maybe I mixed up flat and per-hour. Wait, the problem says: "Peppy Pets charges a flat fee of $15 plus $3 per hour" – so flat is 15, per hour 3: \( 15 + 3x \) or \( 3x + 15 \). "Happy Hounds charges a flat fee of $21 plus $1 per hour" – flat 21, per hour 1: \( 21 + x \) or \( x + 21 \). So the equation is \( 3x + 15 = x + 21 \), which is the fourth option. Wait, but the first option is \( 15x + 3 = 21x + 1 \) – that would be if Peppy was $15 per hour + $3 flat, which is opposite. So the correct equation is \( 3x + 15 = x + 21 \), which is the last option? Wait, the options are:

1. \( 15x + 3 = 21x + 1 \)

1. \( 18x = 22x \)

1. \( 3x + 15 + 21x = 1 \)

1. \( 3x + 15 = x + 21 \)

Yes, the fourth option is correct. Wait, but let's re-express the problem. Wait, maybe I made a mistake. Let's re-express:

Peppy: flat $15 + $3 per hour: total = 15 + 3x.

Happy: flat $21 + $1 per hour: total = 21 + x.

Set equal: 15 + 3x = 21 + x. Which is equivalent to 3x + 15 = x + 21 (just rearranged). So that's the fourth option.

Answer:

The correct equation is \( 3x + 15 = x + 21 \) (the fourth option, assuming the options are ordered as given: first, second, third, fourth, with the fourth being \( 3x + 15 = x + 21 \)).