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ivann1987 [24]
3 years ago
13

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?
Mathematics
1 answer:
solong [7]3 years ago
5 0

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

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