Question 803306
{{{1.18x + 1.15y + 1.09z = 11244.25}}}.......eq.1
{{{3.54x - .55y + .27z = 3732.75}}}.......eq.2
{{{.06x + .05y + .03z = 414.75}}} .......eq.3........all equations multiply by {{{100}}} to get whole numbers
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{{{118x + 115y + 109z = 1124425}}}.......eq.1
{{{354x - 55y + 27z = 373275}}}.......eq.2
{{{6x + 5y + 3z = 41475}}} .......eq.3
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{{{118x + 115y + 109z = 1124425}}}.......eq.1........multiply by {{{3}}} then subtract eq.2 from eq.1
{{{354x - 55y + 27z = 373275}}}.......eq.2
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{{{354x + 345y + 327z = 3373275}}}.......eq.1
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{{{354x - 55y + 27z = 373275}}}.......eq.2
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{{{354x -354x+ 345y+ 55y+ 327z- 27z= 3373275-373275}}}

{{{ 400y+ 300z= 3000000}}}........divide by {{{100}}}

{{{4y+ 3z= 30000}}} .........solve for {{{y}}}

{{{4y = 30000-3z}}}

{{{y = 30000/4-3z/4}}}

{{{y = 7500-0.75z}}}....................eq.1a

go to
{{{6x + 5y + 3z = 41475}}} .......eq.3......plug in eq.1a

{{{6x + 5(7500-0.75z) + 3z = 41475}}} 

{{{6x + 37500-3.75z + 3z = 41475}}} 

{{{6x + 37500-0.75z  = 41475}}} 

{{{6x = 0.75z+41475-37500}}}.......solve for {{{x}}}

{{{6x = 0.75z+3975}}}

{{{x = 0.75z/6+3975/6}}}

{{{x = 0.125z+662.5}}}...............eq1b



go to {{{354x - 55y + 27z = 373275}}}.......eq.2......plug in eq.1a and eq.1b

{{{354(0.125z+662.5)  - 55(7500-0.75z)  + 27z = 373275}}}............solve for {{{z}}}

{{{44.25z+234525-412500+41.25z+ 27z = 373275}}}

{{{44.25z+41.25z+ 27z = 373275-234525+412500}}}

{{{112.5z = 551250}}}

{{{z = 551250/112.5}}}

{{{highlight(z = 4900)}}}..........now find {{{x}}} and {{{y}}}

{{{x = 0.125z+662.5 }}}

{{{x = 0.125*4900+662.5}}} 

{{{x = 612.5+662.5 }}}

{{{highlight(x = 1275)}}}

{{{y = 7500-0.75z}}}

{{{y = 7500-0.75*4900}}}

{{{y = 7500-3675}}}

{{{highlight(y =3825)}}}

so, he borrows 
{{{highlight(x = 1275)}}} dollars on his Mastercard, 
{{{highlight(y =3825)}}} dollars on his Visa Card, 
{{{highlight(z = 4900)}}} dollars on his American Express card