SOLUTION: The time required for a skilled worker to produce x shirts is given by the function T(x) = 4x + 2, where T is measured in hours. The salary the she is paid is given by the function

Question 1151573: The time required for a skilled worker to produce x shirts is given by the function T(x) = 4x + 2, where T is measured in hours. The salary the she is paid is given by the function S(T) = 15T, where S is measured in dollars.
A. If the worker produces 18 units, what will she be paid?
B. How many units would the worker need to produce to be paid $3,030?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Part A
Plug x = 18 into the T(x) function.
T(x) = 4x+2
T(18) = 4*18+2
T(18) = 72+2
T(18) = 74
It takes 74 hours to make 18 shirts.

Plug T = 74 into the S(T) function.
S(T) = 15*T
S(74) = 15*74
S(74) = 1110
The worker will be paid $1,110 for working 74 hours (assuming they are paid the same amount per hour and overtime pay is not involved)

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Alternative Method:

S(T) = 15*T
S(T(x)) = 15*( T(x) )
S(T(x)) = 15*( 4x+2 )
S(T(x)) = 60x+30
E(x) = 60x+30
This function allows us to compute the amount earned in one step, rather than two, based on the x value.

Plug x = 18 into this new function
E(x) = 60x+30
E(18) = 60*18+30
E(18) = 1080+30
E(18) = 1110
We get the same result as before.

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Answer: 1110 dollars.

===========================================
Part B

Method 1) Replace E(x) with 3030 and solve for x
E(x) = 60x+30
3030 = 60x+30
3000 = 60x
60x = 3000
x = 3000/60
x = 50

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Method 2)
Determine how many hours it would take if the worker is paid 3030 dollars
So we want to find T when S = 3030
S(T) = 15T
3030 = 15T
15T = 3030
T = 3030/15
T = 202
It will take 202 hours for the worker to earn 3030 dollars (ignoring things like overtime)

With T = 202, determine the number of shirts that can be made in this time constraint.
T(x) = 4x+2
202 = 4x+2
202-2 = 4x
4x = 200
x = 200/4
x = 50
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Answer: 50 shirts

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