Question

The equation y = 16.50x describes the amount of money Joey earns, where x is the number of hours he works and y is the amount of money he earns.

The table shows the amount of money Kaylee earns for different numbers of hours worked.
Kaylee’s Earnings
Time (h) 2 5 8 10
Money earned ($) 39 97.50 156 195
(a) How much money does Kaylee earn per hour? Show your work.


(b) Who earns more per hour? Justify your answer.

Answer 1

(a)19.5 per hour

(b)Kaylee earns more per hour.

Explanation:

a.) To find the unit rate/hourly rate :

39÷2=19.5 per hour.

b.)Kaylee eanrs more considering that Joey earns 16.50$ per hour as opposed to 19.50$ per hour.

Answer 2

(a) Kaylee earns $19.50 per hour.

(b) Kaylee earns more money per hour than Joey.

Explanation:

x = # of hrs. worked

y = amount of money earned

Joey:

y = 16.50x

Kaylee:

Time (h) 2, 5, 8, 10

Money earned ($) 39, 97.50, 156, 195

y = mx + b; Slope (m) =
`(y_2-y_1)/(x_2-x_1)`

We will be using: (2,39) and (8,156) to find the slope of this table.

`m=(y_2-y_1)/(x_2-x_1) \\\\m=(156-39)/(8-2) \\\\m=(117)/(6) \\\\m=19.5`

y = mx + b

y = 19.5x + b

I will be using (2, 39) to find the value of b

(2, 39)

y = 19.5x + b

39 = 19.5(2) + b

39 = 39 + b

-39 -39

0 = b

y = 19.5x + b ==> y = 17.7x + 0 = OR y = 19.5x (since the value of b is 0)

(a) The question wants us to find out how money Kaylee earns per hour. Recall that x = # of hrs. worked and y = amount of money earned.

y = 19.5x

She earns $19.50 per hour.

(b)

Joey: y = 16.50x (earns $16.50 per hour)

Kaylee: y = 19.5x (earns $19.50 per hour)

As you can see, Kaylee earns more money per hour than Joey.

Hope this helps!