Cara is making punch for a party. She wants to combine 20% real fruit juice drink with a 100% real fruit juice drink to get 16 cups of a mixture that is 80% real fruit juice. How much of each type of drink should she use?

Question

Cara is making punch for a party.  She wants to combine 20% real fruit juice drink with a 100% real fruit juice drink to get 16 cups of a mixture that is 80% real fruit juice. How much of each type of drink should she use?

anonymous · Answer

lets put $x$ as the amount of 100% juice then the amount of 20% juice is $16-x$ since the total is 16

anonymous · Answer

you want to have 80% of 16 = 12.8 real juice, so solve 
$$x+.2(16-x)=12.8$$ for $x$

anonymous · Answer

probably easier to multiply by 10 and solve 
$$10x+2(16-x)=128$$

anonymous · Answer

$$10x+32-2x=128$$
$$8x+32=128$$ two more steps and you are done

anonymous · Answer

x would equal 12

anonymous · Answer

yes, so 12 cups of real juice and the rest (4 cups) or 20% juice

anonymous · Answer

Thank you satellite73!