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Out of a total $x$ games, a basketball team won 21 more than it lost.
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23 Aug 2025, 00:45
23 Aug 2025, 00:45
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Out of a total $x$ games, a basketball team won 21 more than it lost. If the number of games lost is one-third of the total games played, how many games did the team win?
Show: ::
42
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Re: Out of a total $x$ games, a basketball team won 21 more than it lost.
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31 Aug 2025, 10:10
31 Aug 2025, 10:10
Expert Reply
Let:
- $x=$ total number of games played,
- The number of games lost $\(=\frac{1}{3} x\)$.
According to the problem, the basketball team won 21 more games than it lost. So the number of games won is:
$$
\(\text { games won }=\text { games lost }+21=\frac{1}{3} x+21\)
$$
Since the total number of games equals the sum of games won and lost:
$$
\(x=\text { games won }+ \text { games lost }=\frac{1}{3} x+21+\frac{1}{3} x=\frac{2}{3} x+21\)
$$
Rearranging:
$$
\(\begin{gathered}
x-\frac{2}{3} x=21 \\
\frac{1}{3} x=21 \\
x=63
\end{gathered}\)
$$
The number of games won is:
$$
\(\frac{1}{3} x+21=21+21=42\)
$$
Answer: The team won 42 games.
- $x=$ total number of games played,
- The number of games lost $\(=\frac{1}{3} x\)$.
According to the problem, the basketball team won 21 more games than it lost. So the number of games won is:
$$
\(\text { games won }=\text { games lost }+21=\frac{1}{3} x+21\)
$$
Since the total number of games equals the sum of games won and lost:
$$
\(x=\text { games won }+ \text { games lost }=\frac{1}{3} x+21+\frac{1}{3} x=\frac{2}{3} x+21\)
$$
Rearranging:
$$
\(\begin{gathered}
x-\frac{2}{3} x=21 \\
\frac{1}{3} x=21 \\
x=63
\end{gathered}\)
$$
The number of games won is:
$$
\(\frac{1}{3} x+21=21+21=42\)
$$
Answer: The team won 42 games.
gmatclubot
Re: Out of a total $x$ games, a basketball team won 21 more than it lost. [#permalink]
31 Aug 2025, 10:10
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