Example $3\mathrm{.}3$D: Making the Party Punch

In preparing for a party, Brendan needs to mix a punch consisting of fruit juice, vodka, and $7$UP in the ratio of $5$:$3$:$2,$ respectively. If Brendan has a $2L$ bottle of vodka, how much fruit juice and $7$UP must he mix with it$?$

The relationship between the punch recipe ingredients of fruit juice, vodka, and $7$UP forms a ratio. If you set up a similar ratio for what Brendan actually has and needs, you can calculate the exact amounts of fruit juice, vodka, and $7$UP that are required.