To find out how many goals Sydney needs to score to have an equivalent fraction to Brad’s 4 out of 5 goals, we want to set up the equivalent ratio based on her 10 kicks.
Brad's successful goals can be represented as a fraction:
\[ \text{Brad's goals} = \frac{4}{5} \]
We want Sydney to have the same fraction of successful goals, expressed over her 10 kicks:
\[ \text{Sydney's goals} = \frac{x}{10} \]
We set these two fractions equal to each other to find the value of \(x\):
\[ \frac{4}{5} = \frac{x}{10} \]
To solve for \(x\), we can cross-multiply:
\[ 4 \times 10 = 5 \times x \]
This simplifies to:
\[ 40 = 5x \]
Now, divide both sides by 5:
\[ x = \frac{40}{5} = 8 \]
Therefore, Sydney needs to make 8 goals out of 10 kicks to have an equivalent fraction to Brad's 4 out of 5.