SOLUTION: Ben bought a pad of paper, a pencil, an eraser, and a compass for $1.80. The compass cost twice as much as the paper. The eraser cost a third as much as the compass. The pencil

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Question 29935: Ben bought a pad of paper, a pencil, an eraser, and a compass for $1.80. The compass cost twice as much as the paper. The eraser cost a third as much as the compass. The pencil cost half as much as the eraser. How much did each item cost?
Found 2 solutions by Cintchr, Paul:
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
Ohh ... I like this one. First lets define what we know.
+paper+=+a+
+pencil+=+%281%2F2%29eraser+
+eraser+=+%281%2F2%29compass+
+compass+=+2paper+
+paper+%2B+pencil+%2B+eraser+%2B+compass+=+1.80+
now we are going to do some substitution
+paper+%2B+pencil+%2B+eraser+%2B+compass+=+1.80+
where we see "pencil" plug in (1/2)eraser
+paper+%2B+%281%2F2%29eraser+%2B+eraser+%2B+compass+=+1.80+
where we see "eraser" we plug in (1/2)compass
+paper+%2B+%281%2F2%29%281%2F2%29compass+%2B+%281%2F2%29compass+%2B+compass+=+1.80+
where we see "compass" we plug in 2paper
+paper+%2B+%281%2F2%29%281%2F2%292paper+%2B+%281%2F2%292paper+%2B+2paper+=+1.80+
where we see "paper" plug in 'a'
+1a+%2B+%281%2F2%29%281%2F2%292a+%2B+%281%2F2%292a+%2B+2a+=+1.80+
multiply the parts with multiple numbers
+1a+%2B+%281%2F2%29a+%2B+1a+%2B+2a+=+1.80+ now add up the 'a'
+9a%2F2+=+1.80+ have to go to an improper fraction here not a mixed number. change $1.80 to to 9/5 in fraction form.
+9a%2F2+=+9%2F5+ multiply both sides by 2/9
+%289a%2F2%29%282%2F9%29+=+%289%2F5%29%282%2F9%29+ cancel and reduce
+a+=+2%2F5+or+4%2F10+or+.4+
lets look back at our given info:
+paper+=+a+=+.40+
+compass+=+2paper+=+2%28.40%29+=+.80+
+eraser+=+%281%2F2%29compass+=+%281%2F2%29%28.80%29+=+.40+
+pencil+=+%281%2F2%29eraser+=+%281%2F2%29%28.40%29+=+.20+
plug theese values in to the final equation
+paper+%2B+pencil+%2B+eraser+%2B+compass+=+1.80+
+.40+%2B+.20+%2B+.40+%2B+.80+=+1.80+
+1.80+=+1.80+ YES!! we did it right!



Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the paper be x
Let the compass be 2x
Eraser = 3(2x)
Pencil = 6x/2

Total:

2%28x%2F1%29%2B2%282x%2F1%29%2B2%286x%2F1%29%2B2%286x%2F2%29=2%281.8%2F1%29


x=0.15 (paper)
2(0.15)=0.3 (compass)

3(0.3)=0.9 (eraser)

6(0.15)/2=0.45 (pencil)

Hence, the paper is for $0.15, a pencil is for $0.45, a eraser is for $0.9 and a compass is for $0.3
Paul.