2003 AMC 8 Problem 4

Below is the professionally curated solution for Problem 4 of the 2003 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 8 solutions, or check the answer key.

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Concepts:system of equations

Difficulty rating: 720

A group of children riding on bicycles and tricycles rode past Billy Bob's house. Billy Bob counted $7$ children and $19$ wheels. How many tricycles were there?

$2$

$4$

$5$

$6$

$7$

Solution:

Let $b$ be the number of bicycles and $t$ be the number of tricycles. Then we can set up the following system of equations: $\begin{gather*} b + t = 7, \\ 2b + 3t = 19. \end{gather*}$ Multiplying the first equation by $2$ and subtracting from the second equation, we get $t = 5.$

Thus, C is the correct answer.

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