Question

solve for y:
\frac{4}{5} = \frac{y + 6}{15}
simplify your answer as much as possible.

Explanation:

Step1: Cross - multiply to eliminate fractions

To solve the equation \(\frac{4}{5}=\frac{y + 6}{15}\), we can cross - multiply. Cross - multiplying gives us \(4\times15=5\times(y + 6)\).

Step2: Simplify both sides of the equation

First, calculate the left - hand side: \(4\times15 = 60\).
Then, expand the right - hand side: \(5\times(y + 6)=5y+30\). So our equation becomes \(60 = 5y+30\).

Step3: Isolate the variable term

Subtract 30 from both sides of the equation: \(60-30=5y + 30-30\).
Simplifying both sides, we get \(30 = 5y\).

Step4: Solve for y

Divide both sides of the equation by 5: \(\frac{30}{5}=\frac{5y}{5}\).
Simplifying, we find that \(y = 6\).

Answer:

\(y = 6\)