Linear Equations
n = notebook
p = a package of pencils
m = marker
Equations:
Stan:
[tex]\tt n+3p+2m=7.5\:(1)[/tex]
Jan:
[tex]\tt 2n+6p+5m=15.5\:(2)[/tex]
Fran:
[tex]\tt n+2p+2m=6.25\:(3)[/tex]
1&3(elimination)
[tex]\tt n+3p+2m=7.5\\\\n+2p+2m=6.25\\===========\:-\\\\\boxed{\tt p=1.25}[/tex]
2&3(elimination)
[tex]\tt 2n+6p+5m=15.5\times 1\\\\n+2p+2m=6.25\times 2\\===========\:-\\\\2n+6p+5m=15.5\\\\2n+4p+4m=12.5\\===========\:-\\\\2p+m=3\rightarrow p=1.25\\\\2(1.25)+m=3\rightarrow m=3-2.5=\boxed{\tt m=0.5}[/tex]
(1)substitution
[tex]\tt n+3(1.25)+2(0.5)=7.5\rightarrow \boxed{\tt n=2.75}}[/tex]
an individual notebook cost: $2.75
a package of pencils cost: $1.25
an individual marker cost: $0.5
