document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151573>Question 1151573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.\r<BR>\n" );
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document.write( "A. If the worker produces 18 units, what will she be paid?\r<BR>\n" );
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document.write( "B. How many units would the worker need to produce to be paid $3,030? </SPAN>\n" );
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document.write( "Part A<BR>\n" );
document.write( "Plug x = 18 into the T(x) function.<BR>\n" );
document.write( "T(x) = 4x+2<BR>\n" );
document.write( "T(18) = 4*18+2<BR>\n" );
document.write( "T(18) = 72+2<BR>\n" );
document.write( "T(18) = 74<BR>\n" );
document.write( "It takes 74 hours to make 18 shirts.\r<BR>\n" );
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document.write( "Plug T = 74 into the S(T) function.<BR>\n" );
document.write( "S(T) = 15*T<BR>\n" );
document.write( "S(74) = 15*74<BR>\n" );
document.write( "S(74) = 1110<BR>\n" );
document.write( "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)\r<BR>\n" );
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document.write( "Alternative Method:\r<BR>\n" );
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document.write( "S(T) = 15*T<BR>\n" );
document.write( "S(T(x)) = 15*( T(x) )<BR>\n" );
document.write( "S(T(x)) = 15*( 4x+2 )<BR>\n" );
document.write( "S(T(x)) = 60x+30<BR>\n" );
document.write( "E(x) = 60x+30<BR>\n" );
document.write( "This function allows us to compute the amount earned in one step, rather than two, based on the x value.\r<BR>\n" );
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document.write( "Plug x = 18 into this new function<BR>\n" );
document.write( "E(x) = 60x+30<BR>\n" );
document.write( "E(18) = 60*18+30<BR>\n" );
document.write( "E(18) = 1080+30<BR>\n" );
document.write( "E(18) = 1110<BR>\n" );
document.write( "We get the same result as before.\r<BR>\n" );
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document.write( "<font color=red>Answer: 1110 dollars.</font>\r<BR>\n" );
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document.write( "Part B\r<BR>\n" );
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document.write( "Method 1) Replace E(x) with 3030 and solve for x<BR>\n" );
document.write( "E(x) = 60x+30<BR>\n" );
document.write( "3030 = 60x+30<BR>\n" );
document.write( "3000 = 60x<BR>\n" );
document.write( "60x = 3000<BR>\n" );
document.write( "x = 3000/60<BR>\n" );
document.write( "x = 50\r<BR>\n" );
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document.write( "Method 2)<BR>\n" );
document.write( "Determine how many hours it would take if the worker is paid 3030 dollars<BR>\n" );
document.write( "So we want to find T when S = 3030<BR>\n" );
document.write( "S(T) = 15T<BR>\n" );
document.write( "3030 = 15T<BR>\n" );
document.write( "15T = 3030<BR>\n" );
document.write( "T = 3030/15<BR>\n" );
document.write( "T = 202<BR>\n" );
document.write( "It will take 202 hours for the worker to earn 3030 dollars (ignoring things like overtime)\r<BR>\n" );
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document.write( "With T = 202, determine the number of shirts that can be made in this time constraint.<BR>\n" );
document.write( "T(x) = 4x+2<BR>\n" );
document.write( "202 = 4x+2<BR>\n" );
document.write( "202-2 = 4x<BR>\n" );
document.write( "4x = 200<BR>\n" );
document.write( "x = 200/4<BR>\n" );
document.write( "x = 50<BR>\n" );
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document.write( "<font color=red>Answer: 50 shirts</font><BR>\n" );
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