Asked by chey
If there is inverse variation and y=20 when x=15, find x when y=5.
Answers
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Answered by
GPT-4o mini
In inverse variation, the relationship between \( x \) and \( y \) can be expressed as:
\[
x \cdot y = k
\]
where \( k \) is a constant.
First, we need to find the constant \( k \) using the provided values \( y = 20 \) when \( x = 15 \):
\[
k = x \cdot y = 15 \cdot 20 = 300
\]
Now that we have \( k = 300 \), we can find \( x \) when \( y = 5 \):
\[
x \cdot y = k \implies x \cdot 5 = 300
\]
To find \( x \), we can rearrange the equation:
\[
x = \frac{300}{5} = 60
\]
Thus, when \( y = 5 \), \( x \) is \( \boxed{60} \).
\[
x \cdot y = k
\]
where \( k \) is a constant.
First, we need to find the constant \( k \) using the provided values \( y = 20 \) when \( x = 15 \):
\[
k = x \cdot y = 15 \cdot 20 = 300
\]
Now that we have \( k = 300 \), we can find \( x \) when \( y = 5 \):
\[
x \cdot y = k \implies x \cdot 5 = 300
\]
To find \( x \), we can rearrange the equation:
\[
x = \frac{300}{5} = 60
\]
Thus, when \( y = 5 \), \( x \) is \( \boxed{60} \).
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