Question

the amount of a persons paycheck p varies directly with the numbers of hours worked t. for 16 hours of work, the paycheck is $124.00 write a equation for the relationship between hours of work and pay

Answer 1

Given:

Let t = number of hours worked
Let p = money in the paycheck

And the relationship between the two variables varies DIRECTLY, thus they are equated with one another.

Well anyway, you can write this simple equation for their relationship:

16t=124p

Then you derive if you want to get the number of hours or the amount paid:

1) 16t/16= 124p
t = 124p/16
t=7.75p

or

2) 124p=16t
124p/124= 16t/124
p = 0.129t

Answer 2

`p=7.75t`

Explanation:

We have been given that the amount of a persons paycheck p varies directly with the numbers of hours worked t.

Since we know that the equation for direct variation is in form:
`y=kx`, where, k represents the constant of variation.

We are also told that for 16 hours of work, the paycheck is $124.00. We can represent our given information as:

`p=k*t`

Upon substituting p=124 and t=16 in directly proportional equation we will get,

`124=k*16`

Let us divide both sides of our equation by 16 to solve for k.

`(124)/(16)=(k*16)/(16)`

`7.75=k`

Upon substituting the value of constant of variation in our equation we will get,

`p=7.75t`

Therefore, the equation
`p=7.75t` represents the relationship between hours of work and pay.