1997 PMWC Problems/Problem I6

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Problem

John and Mary went to a book shop and bought some exercise books. They had $\$ 100 each. John could buy 7 large and 4 small ones. Mary could buy 5 large and 6 small ones and had $\$ 5 left. How much was a small exercise book?

Solution

$7l+4s=100$

$5l+6s=95$

$2l-2s=5$

$6s-6l=-15$

$11l=110$

$l=10$

$s=\dfrac{15}{2}$

Plugging them back in, we see that they work.

1997 PMWC (Problems)
Preceded by Problem I5	Followed by Problem I7
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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1997 PMWC Problems/Problem I6

From AoPSWiki

Problem

Solution

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