Question

Roberto is having his house painted. the job takes three days, and he pays the painter the same hourly rate every day. the cost of the job is in the chart below. which of the following equations, where h hh represents hours worked and p pp the amount paid in dollars, represent an hourly pay rate that is greater than the painter's hourly rate? day 1 11 day 2 22 day 3 33 hours worked 5 55 4 44 6 66 amount paid $ 300 $300dollar sign, 300 $ 240 $240dollar sign, 240 $ 360 $360dollar sign, 360 choose all answers that apply: choose all answers that apply: (choice a) p = 6.5 h p=6.5hp, equals, 6, point, 5, h a p = 6.5 h p=6.5hp, equals, 6, point, 5, h (choice b) p = 50 h p=50hp, equals, 50, h b p = 50 h p=50hp, equals, 50, h (choice c) p = 65 h p=65hp, equals, 65, h c p = 65 h p=65hp, equals, 65, h (choice d) p = 70 h p=70hp, equals, 70, h d p = 70 h

Answer 1

p=60h

Explanation:

A relationship between two variables, x and y, is said to reflect a proportional variation if it can be written as y/x=ky/x=k or y=kxy=kx.

In a proportional relationship, the proportionality constant, k, is equal to the line's slope, m, and the line also goes through the origin.

Consider,

a = the number of hours worked

b = the amount paid in dollars

In this problem we have a proportional variation, between two variables, a, and b

Find out the constant of proportionality k

For (5,300)⇒ k=b/ak=b/a ⇒ k=300/5=60$/h

For (4,240) ⇒ k=b/ak=b/a ⇒ k=240/4 = 60$/h

For (6,360) ⇒ k=b/ak=b/a ⇒ k=360/6= 60$/h

We can tell that the constant k = 60$/h

Then the equation implies:

b=60ab=60a

The proportionality constant or slope of the linear equation is equal to the unit rate of change of dollars with regard to time.

Therefore the painter paid for one hour work is $60 per hour.