2007 AMC 10A Problems/Problem 5
Contents
[hide]Problem
The school store sells 7 pencils and 8 notebooks for . It also sells 5 pencils and 3 notebooks for
. How much do 16 pencils and 10 notebooks cost?
Solution
Let be cost of one pencil in dollars and
the cost of one notebook in dollars. Then
Subtracting these equations yields . Solving backwards gives
. Thus the answer is
.
Solution 2
Since 5 pencils and 3 notebooks cost 1.77 dollars, then 3 times that or 15 pencils and 9 notebooks costs 5.31 dollars which is 1 pencil and 1 notebook off. Looking at answer choices, it can only be 5.84 so .
Note: 6.00 dollars would imply that 1 pencil and 1 notebook would cost more than 30% of 5 pencils and 3 notebooks, which is incorrect.
See Also
2007 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.