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

A. $1,110

B. 50 units.

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=(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=(200)/(4)\\\\x=50`

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