SOLUTION: please help me to solve Pencils cost 25 cents apiece. Pens cost 80 cents apiece. Susan spent $20 for a total of 36 pens and pencils. How many pencils did she buy? thank you!

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: please help me to solve Pencils cost 25 cents apiece. Pens cost 80 cents apiece. Susan spent $20 for a total of 36 pens and pencils. How many pencils did she buy? thank you!      Log On


   

Question 63629This question is from textbook An Incremental Development
: please help me to solve
Pencils cost 25 cents apiece. Pens cost 80 cents apiece. Susan spent $20 for a total of 36 pens and pencils. How many pencils did she buy?
thank you! This question is from textbook An Incremental Development

Answer by joyofmath(189) About Me  (Show Source):
You can put this solution on YOUR website!
Pencils cost 25 cents apiece. Pens cost 80 cents apiece. Susan spent $20 for a total of 36 pens and pencils. How many pencils did she buy?


Let P = number of pencils.
Let E = number of pens.
Susan spent $20 dollars on 36 pens and pencils so we know:
25P%2B80E+=+2000.
We also know that Susan bought 36 things so we also know:
P%2BE=36 or P=36-E.
Substitute P with 36-E in the first equation:
25%2836-E%29%2B80E+=+2000.
So, %2825%29%2836%29-25E%2B80E+=+2000.
Or, 900%2B55E+=+2000.
So, 55E+=+1100 or E=20.
So, Susan bought 20 pens. She must have then bought 16 pencils since she bought 36 things altogether.
We verify these numbers by noting that 20 pens cost 20*80 = $16 and 16 pencils cost 16*.25 = $4 and the total is $20.