Pregunta
Solve the proportion. \[ \begin{array}{l}\frac{14}{10}=\frac{y+9}{15} \\ y=[?]\end{array} \]
Ask by Ramirez Rowe. in the United States
Jan 20,2025
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\( y = 12 \)
Solución
Solve the equation \( \frac{14}{10}=\frac{y+9}{15} \).
Solve the equation by following steps:
- step0: Solve for \(y\):
\(\frac{14}{10}=\frac{y+9}{15}\)
- step1: Reduce the fraction:
\(\frac{7}{5}=\frac{y+9}{15}\)
- step2: Swap the sides:
\(\frac{y+9}{15}=\frac{7}{5}\)
- step3: Multiply both sides of the equation by \(15:\)
\(\frac{y+9}{15}\times 15=\frac{7}{5}\times 15\)
- step4: Multiply the terms:
\(y+9=\frac{7\times 15}{5}\)
- step5: Evaluate:
\(y+9=21\)
- step6: Move the constant to the right side:
\(y=21-9\)
- step7: Subtract the numbers:
\(y=12\)
The solution to the proportion is \( y = 12 \).
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Bonus Knowledge
To solve the proportion \(\frac{14}{10}=\frac{y+9}{15}\), we can cross-multiply: \[14 \times 15 = 10 \times (y + 9).\] This simplifies to: \[210 = 10y + 90.\] Next, we can isolate \(y\) by first subtracting 90 from both sides: \[210 - 90 = 10y,\] \[120 = 10y.\] Now, divide both sides by 10: \[y = \frac{120}{10} = 12.\] So, the solution is: \[y = 12.\]
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