document.write( "Question 1208236: Hi
\n" ); document.write( "David jogged for 5 days in a row. Each day he jogged 1.4km more than the day before. At the end of 5 days he jogged a total of 20.6km. How far did he jogged on the 5th day. \n" ); document.write( "

Algebra.Com's Answer #846524 by math_tutor2020(3817) $\"\"$ $\"About$

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\n" ); document.write( "Answer: 6.92 km\r
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\n" ); document.write( "\n" ); document.write( "Work Shown\r
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\n" ); document.write( "\n" ); document.write( "x = amount jogged on day 1 only
\n" ); document.write( "x+1.4 = amount jogged on day 2 only
\n" ); document.write( "(x+1.4)+1.4 = x+2*1.4 = amount jogged on day 3 only
\n" ); document.write( "(x+2*1.4)+1.4 = x+3*1.4 = amount jogged on day 4 only
\n" ); document.write( "(x+3*1.4)+1.4 = x+4*1.4 = amount jogged on day 5 only\r
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\n" ); document.write( "\n" ); document.write( "Add up the expressions mentioned.
\n" ); document.write( "Set the sum equal to 20.6 and solve for x.
\n" ); document.write( "day1+day2+day3+day4+day5 = total
\n" ); document.write( "x+(x+1.4)+(x+2*1.4)+(x+3*1.4)+(x+4*1.4) = 20.6
\n" ); document.write( "(x+x+x+x+x)+(1.4+2*1.4+3*1.4+4*1.4) = 20.6
\n" ); document.write( "5x+1.4(1+2+3+4) = 20.6
\n" ); document.write( "5x+1.4(10) = 20.6
\n" ); document.write( "5x+14 = 20.6
\n" ); document.write( "5x = 20.6-14
\n" ); document.write( "5x = 6.6
\n" ); document.write( "x = 6.6/5
\n" ); document.write( "x = 1.32
\n" ); document.write( "David jogged 1.32 km on day 1.
\n" ); document.write( "He jogged x+4*1.4 = 1.32+4*1.4 = 6.92 km on the 5th day.\r
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\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "day1 = 1.32 km
\n" ); document.write( "day2 = 1.32+1.4 = 2.72 km
\n" ); document.write( "day3 = 1.32+2*1.4 = 4.12 km (or 2.72+1.4 = 4.12)
\n" ); document.write( "day4 = 1.32+3*1.4 = 5.52 km (or 4.12+1.4 = 5.52)
\n" ); document.write( "day5 = 1.32+4*1.4 = 6.92 km (or 5.52+1.4 = 6.92)
\n" ); document.write( "total = 1.32+2.72+4.12+5.52+6.92 = 20.6
\n" ); document.write( "This checksum verifies we have the correct answer.\r
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\n" ); document.write( "\n" ); document.write( "--------------------------------------------------------------------------\r
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\n" ); document.write( "\n" ); document.write( "Another approach\r
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\n" ); document.write( "\n" ); document.write( "We have an arithmetic sequence.
\n" ); document.write( "The first term is a1 = x.
\n" ); document.write( "The common difference is d = 1.4
\n" ); document.write( "Sn = sum of the first n terms
\n" ); document.write( "Sn = (n/2)*(2*a1+d*(n-1))
\n" ); document.write( "Sn = (n/2)*(2x+1.4(n-1))
\n" ); document.write( "Then plug n = 5 into this
\n" ); document.write( "S5 = (5/2)*(2x+1.4(5-1))\r
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\n" ); document.write( "\n" ); document.write( "Set this equal to 20.6 and solve for x.
\n" ); document.write( "(5/2)*(2x+1.4(5-1)) = 20.6
\n" ); document.write( "2.5*(2x+5.6) = 20.6
\n" ); document.write( "5x+14 = 20.6
\n" ); document.write( "The steps to solving this are shown in the previous section.
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