Question 1028682: If one group had 3 car washes, 2 bake sales and 5 dances to make $31, and the next had 5 car washes with 5 bake sales and 7 dances to make $56 and the last group had 7 car washes and 3 bake sales and 10 dances for $59 , how much was each cw, bs and d
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! car wash: x
bake sale: y
dances: z
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3x+2y+5z = 31
5x+5y+7z = 56
7x+3y+10z = 59
So now we have a system of equations.
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Multiply the first equation times 5:
(3x+2y+5z = 31)*5 = 15x+10y+25z = 155
Multiply the second equation times 3:
(5x+5y+7z = 56)*3 = 15x+15y+21z = 168
Subtract:
15x+15y+21z = 168
-
15x+10y+25z = 155
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5y-4z = 13
Our new set of equations:
15x+10y+25z = 155
5y-4z = 13
7x+3y+10z = 59
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Multiply the first equation times 7:
(15x+10y+25z = 155)*7 = 105x+70y+175z = 1085
Multiply the third equation times 15:
(7x+3y+10z = 59)*15 = 105x+45y+150z=885
Subtract:
105x+45y+150z=885
-
105x+70y+175z = 1085
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-25y-25z = -200
New set of equations:
105x+70y+175z = 1085
5y-4z = 13
-25y-25z = -200
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Multiply the second equation times 5:
(5y-4z = 13)*5 = 25y-20z=65
Subtract:
-25y-25z = -200
-
25y-20z = 65
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-45z = -135
New set of equations:
105x+70y+175z = 1085
25y-20z = 65
-45z = -135
Solve for z:
-45z = -135 divide both sides by -45 and remember -/- = +
z = 3
Now solve for y:
25y-20(3) = 65
25y-60 = 65
25y = 125
y = 5
Now solve for x:
105x+70y+175z = 1085 you do this one. Email me if you get stock.
John
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