document.write( "Question 1189831: Espano
\n" ); document.write( "Joe the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there
\n" ); document.write( "were 3 clients who did Plan A and 5 who did Plan B. On Tuesday there were 6 clients who did Plan A and 2 who did Plan B. Joe trained his Monday clients for a
\n" ); document.write( "total of 10 hours and his Tuesday clients for a total of 10 hours. How long does each of the workout plans last? \n" ); document.write( "
Algebra.Com's Answer #821362 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "x = length of workout A
\n" ); document.write( "y = length of workout B
\n" ); document.write( "time length durations are in hours\r
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\n" ); document.write( "\n" ); document.write( "Monday:
\n" ); document.write( "3 clients for workout A
\n" ); document.write( "5 clients for workout B
\n" ); document.write( "3x = time for just the plan A people
\n" ); document.write( "5y = time for just the plan B people
\n" ); document.write( "3x+5y = total time for everyone on monday
\n" ); document.write( "3x+5y = 10 hours\r
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\n" ); document.write( "\n" ); document.write( "Tuesday:
\n" ); document.write( "6 clients for plan A
\n" ); document.write( "2 clients for plan B
\n" ); document.write( "6x = time for just the plan A people
\n" ); document.write( "2y = time for just the plan B people
\n" ); document.write( "6x+2y = total time for everyone on tuesday
\n" ); document.write( "6x+2y = 10\r
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\n" ); document.write( "\n" ); document.write( "We found that
\n" ); document.write( "3x+5y = 10
\n" ); document.write( "6x+2y = 10
\n" ); document.write( "for monday and tuesday respectively\r
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\n" ); document.write( "\n" ); document.write( "There are a number of ways we can solve this system of equations.
\n" ); document.write( "I'll use the substitution method. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In this method, there are a few routes as well.
\n" ); document.write( "Let's solve for y in the second equation
\n" ); document.write( "I'm picking this because it means we avoid messy decimals.\r
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\n" ); document.write( "\n" ); document.write( "6x+2y = 10
\n" ); document.write( "2y = 10-6x
\n" ); document.write( "2y = -6x+10
\n" ); document.write( "y = -6x/2+10/2
\n" ); document.write( "y = -3x+5\r
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\n" ); document.write( "\n" ); document.write( "Substitute that into the first equation. Then isolate x.
\n" ); document.write( "3x+5y = 10
\n" ); document.write( "3x+5(-3x+5) = 10
\n" ); document.write( "3x-15x+25 = 10
\n" ); document.write( "-12x+25 = 10
\n" ); document.write( "-12x = 10-25
\n" ); document.write( "-12x = -15
\n" ); document.write( "x = -15/(-12)
\n" ); document.write( "x = 5/4
\n" ); document.write( "x = 1.25
\n" ); document.write( "We get a decimal value, but at least it's not something too crazy.
\n" ); document.write( "Workout A takes 1.25 hours
\n" ); document.write( "aka 1 hour, 15 minutes\r
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\n" ); document.write( "\n" ); document.write( "Then,
\n" ); document.write( "y = -3x+5
\n" ); document.write( "y = -3*1.25+5
\n" ); document.write( "y = -3.75+5
\n" ); document.write( "y = 1.25
\n" ); document.write( "Coincidentally, we get the same value as x.
\n" ); document.write( "It won't always be the case that x = y.\r
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\n" ); document.write( "\n" ); document.write( "Answers:
\n" ); document.write( "Plan A takes 1.25 hours
\n" ); document.write( "Plan B takes 1.25 hours\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "1.25 hours = 1 hr, 15 min
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