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If (2y)/(7)=(y+3)/(4), then y=...

If `(2y)/(7)=(y+3)/(4),` then `y=`

A

`5`

B

`9`

C

`13`

D

`21`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the equation \(\frac{2y}{7} = \frac{y + 3}{4}\), we will follow these steps: ### Step 1: Cross-Multiply To eliminate the fractions, we can cross-multiply: \[ 2y \cdot 4 = (y + 3) \cdot 7 \] This simplifies to: \[ 8y = 7(y + 3) \] ### Step 2: Distribute on the Right Side Next, we distribute \(7\) on the right side: \[ 8y = 7y + 21 \] ### Step 3: Isolate \(y\) Now, we want to isolate \(y\). We can do this by subtracting \(7y\) from both sides: \[ 8y - 7y = 21 \] This simplifies to: \[ y = 21 \] ### Final Answer Thus, the value of \(y\) is: \[ \boxed{21} \]
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