Huang Murray
06/06/2023 · Primary School
16. \( \frac{7}{2}: 10=\frac{7}{3}: x \)
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Tutor-Verified Answer
Step-by-step Solution
To solve the proportion \( \frac{7}{2}: 10=\frac{7}{3}: x \), we can rewrite it in a more manageable form. The expression can be interpreted as:
\[
\frac{\frac{7}{2}}{10} = \frac{\frac{7}{3}}{x}
\]
Cross-multiplying gives us:
\[
\frac{7}{2} \cdot x = \frac{7}{3} \cdot 10
\]
Now, we can simplify the right side:
\[
\frac{7}{3} \cdot 10 = \frac{70}{3}
\]
So we have:
\[
\frac{7}{2} \cdot x = \frac{70}{3}
\]
Next, we can solve for \( x \) by multiplying both sides by the reciprocal of \( \frac{7}{2} \):
\[
x = \frac{70}{3} \cdot \frac{2}{7}
\]
Now, simplify the right side:
\[
x = \frac{70 \cdot 2}{3 \cdot 7} = \frac{140}{21}
\]
Now, simplify \( \frac{140}{21} \):
\[
x = \frac{20}{3}
\]
Thus, the solution is:
\[
\boxed{\frac{20}{3}}
\]
Quick Answer
The solution is \( x = \frac{20}{3} \).
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