Johnson Chambers
11/08/2023 · Junior High School
8. If \( x=2.1 \) when \( y=7.2 \) find \( x \) when \( y=7.56 \)
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Tutor-Verified Answer
Step-by-step Solution
Given that when \( x = 2.1 \), \( y = 7.2 \), we can find the relationship between \( x \) and \( y \) by setting up a proportion.
Let's denote the relationship between \( x \) and \( y \) as \( \frac{x}{y} = \frac{2.1}{7.2} \).
Now, we need to find \( x \) when \( y = 7.56 \). We can set up a proportion using the relationship we found earlier:
\[
\frac{x}{7.56} = \frac{2.1}{7.2}
\]
We can solve this proportion to find the value of \( x \) when \( y = 7.56 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{x}{7.56}=\frac{2.1}{7.2}\)
- step1: Divide the terms:
\(\frac{25x}{189}=\frac{7}{24}\)
- step2: Multiply both sides of the equation by \(189:\)
\(\frac{25x}{189}\times 189=\frac{7}{24}\times 189\)
- step3: Multiply the terms:
\(25x=\frac{7\times 189}{24}\)
- step4: Evaluate:
\(25x=\frac{441}{8}\)
- step5: Multiply by the reciprocal:
\(25x\times \frac{1}{25}=\frac{441}{8}\times \frac{1}{25}\)
- step6: Multiply:
\(x=\frac{441}{200}\)
When \( y = 7.56 \), the value of \( x \) is \( x = \frac{441}{200} \) or \( x = 2.205 \).
Quick Answer
When \( y = 7.56 \), \( x = 2.205 \).
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