Question

The manager at a health foods store mixes a unique superfruit juice cocktail that costs$38.55 per liter to make. The cocktail includes mixed fruit juice and acai berry juice, whichcost $4.15 per liter and $47.15 per liter, respectively. The manager has already opened 19liters of the mixed fruit juice. How many liters of the acai berry juice does he need to add?Write your answer as a whole number or as a decimal rounded to the nearest tenth.

Answer 1

Let m represent the proportion of mixed fruit juice in 1 litre,

The proportion of acai berry in 1 litre will be 1-m

Cost per litre of mixed fruit juice = $4.15

Cost per litre of acai berry juice = $47.15

From the second statement,

4.15m + (1-m)47.15 = 38.55

4.15m + 47.15 - 47.15m = 38.55

4.15m - 47.15m = 38.55 - 47.15

-43m = -8.6

m = -8.6/-43

m = 0.2

For acai berry, we have 1-m

= 1 - 0.2

=0.8

This implies that the ratio of litres of mixed fruit juice to acai berry juice in the superfruit cocktail is

0.2 : 0.8

The manager used 19 litres of mixed fruit juice,

Let y be the number of litres of acai berry used

`\begin{gathered} \text{ 0.2 : 0.8 = 19 : y} \\ (0.2)/(0.8)\text{ = }(19)/(y) \\ 0.2y\text{ =19 x 0.8} \\ 0.2y\text{ =15.2} \\ y=(15.2)/(0.2) \\ y=76 \end{gathered}`

Hence the amount of litres of acai berry juice he needs to add is 76 litres

7