A mechanic worked 20 hours. another mechanic worked 15 hours. together they charged a total of $1950. what was the rate charged per hour for each mechanic if the sum of the two rates were $115 per hour

The mechanics both charged $70 and $45 per hour respectively

Step-by-step explanation: We shall start by calling the mechanics hourly rates x and y respectively. So if one worked for 20 hours and charged 20 times x dollars, and the other one worked for 15 hours and charged 15 times y dollars, totalling 1950 dollars, we can write the following expression,

20x + 15y = 1950

Also, if the sum of the two rates was 115 dollars, that means for working for an hour only, they both would earn

x + y = 115

We now have a pair of simultaneous equations

20x + 15y = 1950 (1)

x + y = 115 (2)

We shall use the substitution method for this problem.

From equation (2), make x the subject of the equation

x = 115 - y

Substitute for the value of x into equation (1)

20(115 - y) + 15y = 1950

2300 - 20y + 15y = 1950

By collecting like terms we now have

2300 - 1950 = 20y - 15y

(Note that when a negative value crosses to the other side of the equation, it becomes a positive value and vice versa)

350 = 5y

Divide both sides of the equation by 5

70 = y

We now substitute for the value of y into equation (2)

x + y = 115

x + 70 = 115

Subtract 70 from both sides of the equation

x = 45.

Therefore, the rate they charged per hour were $45 and $70 respectively.

Question:

Raul works at a movie theatre. The function f(x) represents the amount of money Raul earns per ticket, where x is the number of tickets he sells. The function g(x) represents the number of tickets Raul sells per hour, where x is the number of hours he works. Show all work to find f(g(x)), and explain what f(g(x)) represents.

f(x) = 2x2 + 16

g of x equals the square root of the quantity 5 x cubed

f(g(x))=  

Step-by-step explanation:

Given:

f(x) =

g(x) =

f(x) represents the amount of money Raul earns per ticket

x is the number of tickets he sells

g(x) represents the number of tickets Raul sells per hour

To find:

f(g(x)) = ?

Solution:

f(g(x)) represent the amount Raul earns by selling tickets for x hours

We know,

f(x)  =

f(g(x)) =

The square root and power 2 cancel each other

f(g(x))  =

f(g(x)) =

So at x hours

Raul earns

For example lets assume Raul works for 5 hours, then the amount he earns will be

f(g(x)) =

f(g(x))  = 10(125) +16

f(g(x)) = 1250 +16

f(g(x)) =  1266

You  can also find the amount Raul earns by

g(x) =

g(x) =

g(x) = 25

Substituting in f(x)

f(g(x)) = f(25)

f(25)  =

f(25) = 2(625) +16

f(25) = 1250 + 16

f(25) = 1266

so Raul will be earning 1266 if he sells tickets for 5 hours