2005 PMWC Problems/Problem I14

Problem

George purchases a sack of apples, a bunch of bananas, a cantaloupe, and a carton of dates for $$ 20$ . 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

$3g = 6b \Longrightarrow g = 2b$ $2y = 5b \Longrightarrow y = \frac{5}{2}b$ $4w = 6b \Longrightarrow w = \frac{3}{2}b$

Substuting gives us $4g + 2y + 2w = 4(2b) + 2\left(\frac{5}{2}b\right) + 2\left(\frac{3}{2}b\right) = 16b$ , and our answer is 16.

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

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2005 PMWC Problems/Problem I14

Problem

Solution

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