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al,bill,and carl went shopping
al and bill together spent a total 1,200;
bill and carl spent together 1,800;
al and carl together spent a total 1,000
how much did each person spent

Sagot :

Lanstznridn

Answer:

[tex]\left[\begin{array}{ccc}Al&spent&200\\Bill&spent&1,000\\Carl&spent&800\end{array}\right][/tex]

Step-by-step explanation:

Let x, y, and z represent the amount spent by Al, Bill, and Carl respectively.

[tex]\left[\begin{array}{ccc}Equation1:&x+y=1,200\\Equation2:&y+z=1,800\\Equation3:&x+z=1,000\end{array}\right][/tex]

Simplify x in Eq.1 and substitute value for x in Eq.3 to simplify value for z.

[tex]x+y=1,200\\x=1,200-y[/tex]

[tex]x+z=1,000\\(1,200-y)+z=1,000\\z=1,000-1,200+y\\z=-200+y[/tex]

Substitute -200+y for z in Eq.2 to determine y.

[tex]y+z=1,800\\y+(-200+y)=1,800\\2y=1,800+200\\y=2,000/2=1,000[/tex]

Substitute 1,000 for y in Eq.1 to determine x.

[tex]x+y=1,200\\x+1,000=1,200\\x=1,200-1,000=200[/tex]

Substitute 200 for x in Eq.3 to determine z.

[tex]x+z=1,000\\200+z=1,000\\z=1,000-200=800[/tex]

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