SOLUTION: four pencils and five pens cost $2.00. three pencils and four pens cost $1.58. find the cost of a pencil and the cost of a pen

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: four pencils and five pens cost $2.00. three pencils and four pens cost $1.58. find the cost of a pencil and the cost of a pen      Log On


   

Question 184910: four pencils and five pens cost $2.00.
three pencils and four pens cost $1.58.
find the cost of a pencil and the cost of a pen
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

1st Condiion:
4Pencil%2B5Pens=2.00
2nd Condition:
3Pencils%2B4Pens=1.58
In 1st Condition we get, 4Pencils=2.00-5Pens,
cross%284%29%2APencils%2Fcross%284%29=%282.00-5Pens%29%2F4=%282.00%2F4%29-%285%2F4%29Pens
Pencils=%281%2F2%29-%285%2F4%29Pens,EQN 1
Susbt. EQN 1 in Condition 2:
3%28%281%2F2%29-%285%2F4%29Pens%29%2B4Pens=1.58
%283%2F2%29-%2815%2F4%29Pens%2B4Pens=1.58
%28-15%2B16%29Pens%2F4=1.58-%283%2F2%29
%281%2F4%29Pens=%283.16-3%29%2F2=0.16%2F2
Cross Multiply:
2Pens=4%2A0.16=0.64
cross%282%29%2APens%2Fcross%282%29=cross%280.64%290.32%2Fcross%282%29
highlight%28Pens=0.32%2Feach%29
In EQN 1:--->Pencils=%281%2F2%29-%285%2F4%29%280.32%29=%281%2F2%29-0.40=0.50-0.40
highlight%28Pencils=0.10%2Feach%29
In doubt?, Go back Condition 1:
4%280.10%29%2B5%280.32%29=2.00
0.40%2B1.6=2.00
2.00=2.00
Go back Condition 2:
3%280.10%29%2B4%280.32%29=1.58
0.30%2B1.28=1.58
1.58=1.58
Thank you,
Jojo