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: \( 15 + 3x \) (flat \$15 + \$3 per hour). Happy Hounds: \( 21 + x \) (flat \$21 + \$1 per hour).

Step2: Set costs equal

To find when costs are same, set \( 15 + 3x = 21 + x \). Rearranging (subtract \( x \) and 15): \( 3x - x = 21 - 15 \to 2x = 6 \)? Wait, no—wait the options. Wait the first option: \( 15x + 3 = 21x + 1 \)? No, wait I misread. Wait Peppy: flat \$15 + \$3 per hour: \( 3x + 15 \). Happy: flat \$21 + \$1 per hour: \( x + 21 \). So equation \( 3x + 15 = x + 21 \). Wait the fourth option is \( 3x + 15 = x + 21 \)? Wait the options:

1. \( 15x + 3 = 21x + 1 \) – no, Peppy is 15 flat + 3x, not 15x +3.
2. \( 18x = 22x \) – no.
3. \( 3x +15 +21x =1 \) – no.
4. \( 3x +15 = x +21 \) – yes! Because Peppy: \( 3x +15 \), Happy: \( x +21 \). Set equal: \( 3x +15 = x +21 \). Wait but let's check again. Wait the problem says Peppy Pets charges flat \$15 plus \$3 per hour: so total cost \( C_p = 15 + 3x \). Happy Hounds: flat \$21 plus \$1 per hour: \( C_h = 21 + x \). To find when \( C_p = C_h \), so \( 15 + 3x = 21 + x \), which is \( 3x +15 = x +21 \) (the fourth option). Wait the first option was \( 15x +3 =21x +1 \) – that's if flat was per x, but no. So the correct equation is \( 3x +15 = x +21 \), which is the fourth option. Wait but let's check the options again. Wait the user's options:

First option: \( 15x + 3 = 21x + 1 \)

Second: \( 18x = 22x \)

Third: \( 3x +15 +21x =1 \)

Fourth: \( 3x +15 = x +21 \)

Yes, fourth option is correct. Wait but maybe I messed up. Wait Peppy: flat \$15 (so constant) + \$3 per hour (3x). Happy: flat \$21 (constant) + \$1 per hour (x). So equation: \( 3x +15 = x +21 \). So the fourth option.

Answer:

The correct equation is the fourth option: \( 3x + 15 = x + 21 \) (the bottom - most option among the four given equations).