Question - Direct Variation Problem Solution
Solution:
The image features a mathematical problem that reads: "Given $$ x $$ and $$ y $$ = 65 when $$ x = 5 $$, find $$ y $$ when $$ x = 2 $$."This problem describes a direct variation between $$ x $$ and $$ y $$, where their product is constant. Initially, when $$ x = 5 $$, $$ y $$ is such that $$ x \cdot y = 65 $$.First, we can find the initial value of $$ y $$ when $$ x = 5 $$:\[ 5 \cdot y = 65 \]\[ y = 65 / 5 \]\[ y = 13 \]Now that we know the relationship between $$ x $$ and $$ y $$ is such that their product is always 65, we can use this information to find $$ y $$ when $$ x = 2 $$:\[ x \cdot y = 65 \]\[ 2 \cdot y = 65 \]\[ y = 65 / 2 \]\[ y = 32.5 \]Therefore, when $$ x = 2 $$, $$ y $$ is 32.5.
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