Multiply the second equation by 3: $ 9x + 6y = 54.90 $. Subtract the first equation: $ (9x + 6y) - (4x + 6y) = 54.90 - 32.40 $, yielding $ 5x = 22.50 $. Thus, $ x = 4.50 $ dollars, or $ \boxed{450} $ cents.

February 22, 2026

$Multiply the second equation by 3: $ 9x + 6y = 54.90 $. Subtract the first equation: $ (9x + 6y) - (4x + 6y) = 54.90 - 32.40 $, yielding $ 5x = 22.50 $. Thus, $ x = 4.50 $ dollars, or $ \boxed{450} $ cents.$

Solution: Let $ x $ be the cost of an app icon in dollars and $ y $ the cost of a color theme. The system of equations is:
4x + 6y = 32.40 \\
3x + 2y = 18.30
Question: An archaeologist discovers 5 pottery shards and 2 stone tools worth \$48.50, and 3 pottery shards and 4 stone tools worth \$51.00. What is the value of one stone tool in dollars?
Solution: Let $ p $ be the price of a pottery shard and $ s $ the price of a stone tool. The system is:
5p + 2s = 48.50 \\

Multiply the second equation by 3: $ 9x + 6y = 54.90 $. Subtract the first equation: $ (9x + 6y) - (4x + 6y) = 54.90 - 32.40 $, yielding $ 5x = 22.50 $. Thus, $ x = 4.50 $ dollars, or $ \boxed{450} $ cents.

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