Question - Direct Variation Problem Solution
Solution:
The image shows a direct variation problem where $$ y $$ is directly proportional to $$ x $$. It states that $$ y = 10 $$ when $$ x = 14 $$ and asks for the value of $$ y $$ when $$ x = 21 $$.In such problems, the ratio $$ y/x $$ remains constant, so we have:\[ \frac{y_1}{x_1} = \frac{y_2}{x_2} \]Given $$ y_1 = 10 $$ and $$ x_1 = 14 $$, we can express $$ y_2 $$ in terms of $$ x_2 = 21 $$ using the direct variation formula:\[ \frac{10}{14} = \frac{y_2}{21} \]To find $$ y_2 $$, we solve:\[ y_2 = \frac{10}{14} \times 21 \]\[ y_2 = \frac{10 \times 21}{14} \]Now simplify the fraction:\[ y_2 = \frac{10 \times 3}{2} \]\[ y_2 = \frac{30}{2} \]\[ y_2 = 15 \]Hence when $$ x = 21 $$, $$ y = 15 $$.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com