SOLUTION: I) An owner of a small business borrows money on three separate credit cards. X dollars on his Mastercard, y dollars on his Visa Card, z dollars on his American Express card. These

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I) An owner of a small business borrows money on three separate credit cards. X dollars on his Mastercard, y dollars on his Visa Card, z dollars on his American Express card. These      Log On


   



Question 803306: I) An owner of a small business borrows money on three separate credit cards. X dollars on his Mastercard, y dollars on his Visa Card, z dollars on his American Express card. These amount satisfy the following equations.

1.18x + 1.15y + 1.09z = 11,244.25
3.54x - .55y + .27z = 3,732.75
.06x + .05y + .03z = 414.75
How much money did the owner borrow on each card

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1.18x+%2B+1.15y+%2B+1.09z+=+11244.25.......eq.1
3.54x+-+.55y+%2B+.27z+=+3732.75.......eq.2
.06x+%2B+.05y+%2B+.03z+=+414.75 .......eq.3........all equations multiply by 100 to get whole numbers
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118x+%2B+115y+%2B+109z+=+1124425.......eq.1
354x+-+55y+%2B+27z+=+373275.......eq.2
6x+%2B+5y+%2B+3z+=+41475 .......eq.3
_____________________________
118x+%2B+115y+%2B+109z+=+1124425.......eq.1........multiply by 3 then subtract eq.2 from eq.1
354x+-+55y+%2B+27z+=+373275.......eq.2
______________________________
354x+%2B+345y+%2B+327z+=+3373275.......eq.1
-
354x+-+55y+%2B+27z+=+373275.......eq.2
_______________________________
354x+-354x%2B+345y%2B+55y%2B+327z-+27z=+3373275-373275
+400y%2B+300z=+3000000........divide by 100
4y%2B+3z=+30000 .........solve for y
4y+=+30000-3z
y+=+30000%2F4-3z%2F4
y+=+7500-0.75z....................eq.1a
go to
6x+%2B+5y+%2B+3z+=+41475 .......eq.3......plug in eq.1a
6x+%2B+5%287500-0.75z%29+%2B+3z+=+41475
6x+%2B+37500-3.75z+%2B+3z+=+41475
6x+%2B+37500-0.75z++=+41475
6x+=+0.75z%2B41475-37500.......solve for x
6x+=+0.75z%2B3975
x+=+0.75z%2F6%2B3975%2F6
x+=+0.125z%2B662.5...............eq1b


go to 354x+-+55y+%2B+27z+=+373275.......eq.2......plug in eq.1a and eq.1b
354%280.125z%2B662.5%29++-+55%287500-0.75z%29++%2B+27z+=+373275............solve for z
44.25z%2B234525-412500%2B41.25z%2B+27z+=+373275
44.25z%2B41.25z%2B+27z+=+373275-234525%2B412500
112.5z+=+551250
z+=+551250%2F112.5
highlight%28z+=+4900%29..........now find x and y
x+=+0.125z%2B662.5+
x+=+0.125%2A4900%2B662.5
x+=+612.5%2B662.5+
highlight%28x+=+1275%29
y+=+7500-0.75z
y+=+7500-0.75%2A4900
y+=+7500-3675
highlight%28y+=3825%29
so, he borrows
highlight%28x+=+1275%29 dollars on his Mastercard,
highlight%28y+=3825%29 dollars on his Visa Card,
highlight%28z+=+4900%29 dollars on his American Express card