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.
Day 111 Day 222 Day 333
Hours worked 555 444 666
Amount paid \$300$300dollar sign, 300 \$240$240dollar sign, 240 \$360$360dollar sign, 360
What is the painter's unit rate of change of dollars with respect to time; that is, how much is the painter paid for one hour worked?
Answers
Answer:
$60 per hour
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=ky/x=k or y=kxy=kx
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Let
x -----> the number of hours worked
y ----> the amount paid in dollars
In this problem we have a proportional variation, between two variables, x, and y
Find out the constant of proportionality k
For (5,300) -----> k=y/xk=y/x ----> k=300/5=60\ \$/hk=300/5=60 $/h
For (4,240) -----> k=y/xk=y/x ----> k=240/4=60\ \$/hk=240/4=60 $/h
For (6,360) -----> k=y/xk=y/x ----> k=360/6=60\ \$/hk=360/6=60 $/h
The constant k is
k=60\ \$/hk=60 $/h
The equation is equal to
y=60xy=60x
The unit rate of change of dollars with respect to time is equal to the constant of proportionality or slope of the linear equation
therefore
\$60\ per\ hour$60 per hour
The painter paid $60 per hour.
Given:
Day 1 - worked 5 hours - amount paid - $300
Day 2 - worked 4 hours - amount paid - $240
Day 3 - worked 6 hours - amount paid - $360
To find:
Amount paid per hour work = ?
Solution:
Knowing this
A relationship between two variables, x and y, is said to reflect a proportional variation if it can be written as y/x=ky/x=k or y=kxy=kx.
In a proportional relationship, the proportionality constant, k, is equal to the line's slope, m, and the line also goes through the origin.
Consider,
a = the number of hours worked
b = the amount paid in dollars
In this problem we have a proportional variation, between two variables, a, and b
Find out the constant of proportionality k
For (5,300)⇒ k=b/ak=b/a ⇒ k=300/5=60$/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.
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