Question
\( 1 \leftarrow \) Solve the following proportion for the variable b . \[ \begin{array}{l}\frac{13}{14}=\frac{\mathrm{b}}{21} \\ \mathrm{~b}=\square \text { (Type an integer or a simplified fraction.) }\end{array} \]
Ask by Griffin Mcguire. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( b = \frac{39}{2} \) or \( b = 19.5 \).
Solution
Solve the equation \( \frac{13}{14}=\frac{b}{21} \).
Solve the equation by following steps:
- step0: Solve for \(b\):
\(\frac{13}{14}=\frac{b}{21}\)
- step1: Swap the sides:
\(\frac{b}{21}=\frac{13}{14}\)
- step2: Multiply both sides of the equation by \(21:\)
\(\frac{b}{21}\times 21=\frac{13}{14}\times 21\)
- step3: Multiply the terms:
\(b=\frac{13\times 21}{14}\)
- step4: Divide the terms:
\(b=\frac{39}{2}\)
The solution to the proportion is \( b = \frac{39}{2} \) or \( b = 19.5 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
To solve the proportion \(\frac{13}{14}=\frac{b}{21}\), you can cross-multiply. This gives you: \[ 13 \times 21 = 14 \times b \] Calculating the left side: \[ 273 = 14b \] Next, divide both sides by 14 to isolate \(b\): \[ b = \frac{273}{14} \] Now simplify the fraction. 273 divided by 14 equals 19.5, which is also \(\frac{39}{2}\) in fraction form. Therefore, \[ b = 19.5 \, \text{or} \, \frac{39}{2} \] So \( b = \frac{39}{2}\) in its simplified fraction form.
