Difference between revisions of "2005 PMWC Problems/Problem I14"

Revision as of 20:33, 21 August 2022

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.

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 == Problem ==
-On a balance scale, three green balls balance six blue balls, two yellow balls balance five blue balls and six blue balls balance four white balls. How many blue balls are needed to balance four green, two yellow and two white balls?
+George purchases a sack of apples, a bunch of bananas, a cantaloupe, and a carton of dates for <math> \$ 20</math>. 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 ==

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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Difference between revisions of "2005 PMWC Problems/Problem I14"

Revision as of 20:33, 21 August 2022

Problem

Solution

See also