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Kyle has 22 more cards than 3 times the number of cards that Stan owns. Together, they own less than 58 cards. How many cards are in Stan's collection? A) Stan owns 9 cards or less. B) Stan owns 9 cards or more. C) Stan owns less than 9 cards. D) Stan owns more than 9 cards.

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Answer

C) Stan owns less than 9 cards.

Explanation

Let [tex]k[/tex] be the number of Kyle's cards and [tex]s[/tex] the number of Stan's cards.

We know from our problem that Kyle has 22 more cards than 3 times the number of cards that Stan owns, so:

[tex]k=3s+22[/tex] equation (1)

We also knows that together, they own less than 58 cards, so:

[tex]k+s<58[/tex] equation (2)

Replace (1) in (2) and solve for [tex]s[/tex]:

[tex]3s+22+s<58[/tex]

[tex]4s<36[/tex]

[tex]s<\frac{36}{4}[/tex]

[tex]s<9[/tex]

Stan owns less than 9 cards.