2005 PMWC Problems/Problem I14
Problem
George purchases a sack of apples, a bunch of bananas, a cantaloupe, and a carton of dates for 
. If a carton of dates costs twice as much as a sack of apples and the price of a cantaloupe is equal to the price of a sack of apples minus a bunch of bananas, how much would it cost George to purchase a bunch of bananas and a cantaloupe?
Solution
From the given, we have the equations
![\[3g = 6b \Longrightarrow g = 2b\]](http://latex.artofproblemsolving.com/5/f/6/5f60887b227441d3862d1ee98b0432c25813ec90.png)
![\[2y = 5b \Longrightarrow y = \frac{5}{2}b\]](http://latex.artofproblemsolving.com/2/d/5/2d55865cdf8b228c22e55ade16923f969057740e.png)
![\[4w = 6b \Longrightarrow w = \frac{3}{2}b\]](http://latex.artofproblemsolving.com/4/a/f/4af0d778d88d87a3a12b1c1fb704cc0c78650992.png)
Substuting gives us 
, and our answer is 16.
See also
| 2005 PMWC (Problems) | ||
| Preceded by Problem I13 |
Followed by Problem I15 | |
| I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
