Question

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 1

Answer:

A. $1,110

B. 50 units.

Step-by-step explanation:

A. Substitute $x=18$ into the function $T(x)=4x+2$ for calculate the time in hours required for the worker to produce 18 units:

$T(18)=4(18)+2=74$

Now you need to substitute $T=74$ into the function $S(T)=15T$ to calculate the amount in dollars she will be paid for 74 hours:

$S(74)=15(74)=1,110$

She will be paid $1,110.

B. To calculate the number of units that the worker needs to produce to be paid $3,030 , you need to substitute $S(T)=3,030$ into the function $S(T)=15T$ and solve for T (to find the number of hours she requires to work to be paid $3,030)

$3,030=15T\\\\T=\frac{3,030}{15}\\\\T=202$

Now, substitute $T(x)=202$ into $T(x)=4x+2$ and solve for x, to calculate the number of units she produces in 202 hours:

$202=4x+2\\\\202-2=4x\\\\x=\frac{200}{4}\\\\x=50$

She would need to produce 50 units to be paid $3,030