Question

Ari is starting a yard service business. He charges a flat rate of $10 plus an additional $15 per hour, regardless of the service. Create a function and use a table to determine how much Ari will make if he works for 1, 1.5, 2, 2.5, and 3 hours.

A: (15, 1), (17.5, 1.5), ( 20,2), ( 22.5, 2.5), ( 25,3)

B: (1,25), (1.5, 32.5), ( 2,40), ( 2.5, 47.5), ( 3,55)

C: ( 1,16), ( 1.5, 16.5), ( 2, 17) ( 2.5, 17.5), ( 3,18)

D: ( 1,5), (1.5, 7.5), ( 2,10), ( 2.5, 12.5), ( 3,15)

Answer 1

To determine how much Ari will make based on the hours worked, we first need to create the function that represents his earnings. Ari charges a flat rate of $10 plus an additional $15 for each hour worked. The earnings function can be expressed as:

\[ E(h) = 10 + 15h \]

where \( E(h) \) is the total earnings when working for \( h \) hours.

Now, let's calculate the earnings for the given hours: 1, 1.5, 2, 2.5, and 3 hours.

1. For \( h = 1 \):
\[ E(1) = 10 + 15(1) = 10 + 15 = 25 \]

2. For \( h = 1.5 \):
\[ E(1.5) = 10 + 15(1.5) = 10 + 22.5 = 32.5 \]

3. For \( h = 2 \):
\[ E(2) = 10 + 15(2) = 10 + 30 = 40 \]

4. For \( h = 2.5 \):
\[ E(2.5) = 10 + 15(2.5) = 10 + 37.5 = 47.5 \]

5. For \( h = 3 \):
\[ E(3) = 10 + 15(3) = 10 + 45 = 55 \]

Now, we can organize these results into a table:

| Hours Worked (h) | Earnings (E) |
|------------------|--------------|
| 1 | 25 |
| 1.5 | 32.5 |
| 2 | 40 |
| 2.5 | 47.5 |
| 3 | 55 |

Based on these calculations, we can see that the set of ordered pairs for each calculation is:

- (1, 25)
- (1.5, 32.5)
- (2, 40)
- (2.5, 47.5)
- (3, 55)

Looking at the options provided, the correct choice is:

**B: (1, 25), (1.5, 32.5), (2, 40), (2.5, 47.5), (3, 55)**