Bernard Donnelly
02/15/2023 · Elementary School
EXERCISE 21.2 \( 1 y \) is inversely proportional to \( x \), and \( y=20 \) when \( x=5 \). Find the value of \( y \) when \( x=4 \).
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Tutor-Verified Answer
Step-by-step Solution
Since \( y \) is inversely proportional to \( x \), we can express this relationship as:
\[
y = \frac{k}{x}
\]
where \( k \) is a constant.
Given that \( y = 20 \) when \( x = 5 \), we can substitute these values into the equation to find \( k \):
\[
20 = \frac{k}{5}
\]
Multiplying both sides by 5 gives:
\[
k = 20 \times 5 = 100
\]
Now that we have the value of \( k \), we can use it to find \( y \) when \( x = 4 \):
\[
y = \frac{100}{4}
\]
Calculating this gives:
\[
y = 25
\]
Thus, the value of \( y \) when \( x = 4 \) is \( \boxed{25} \).
Quick Answer
\( y = 25 \) when \( x = 4 \).
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