Question
Solve for \( a \) in the proportion. \[ \begin{array}{l}\frac{19}{a}=\frac{9.5}{6} \\ a=\square\end{array} \]
Ask by Cummings Frank. in the United States
Dec 24,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
\( a = 12 \)
Solution
Solve the equation \( 19/a=9.5/6 \).
Solve the equation by following steps:
- step0: Solve for \(a\):
\(\frac{19}{a}=\frac{9.5}{6}\)
- step1: Find the domain:
\(\frac{19}{a}=\frac{9.5}{6},a\neq 0\)
- step2: Divide the terms:
\(\frac{19}{a}=\frac{19}{12}\)
- step3: Rewrite the expression:
\(a=12\)
- step4: Check if the solution is in the defined range:
\(a=12,a\neq 0\)
- step5: Find the intersection:
\(a=12\)
La solución para \( a \) en la proporción dada es \( a = 12 \).
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Simplify this solution Extra Insights
To solve for \( a \) in the proportion \(\frac{19}{a}=\frac{9.5}{6}\), we can cross-multiply. This gives us: \[ 19 \times 6 = 9.5 \times a \] Calculating the left side: \[ 114 = 9.5a \] Now, to isolate \( a \), we divide both sides by 9.5: \[ a = \frac{114}{9.5} \] When we do the division: \[ a = 12 \] Thus, the solution is \( a = 12 \).
