Concentrate 18043

Fruit juice concentrate is sold in two-liter bottles. It is diluted with water in a ratio of 1:9.
a) determine how to prepare 5 liters of fruit drink from concentrate and water.
b) How many liters of fruit drink can be prepared from a full bottle of fruit concentrate

Correct answer:

a₁ =  0.5 l
a₂ =  4.5 l
b =  20 l

Step-by-step explanation:

a₁ = 1/9·a₂
a₁+a₂=5

9a₁-a₂ = 0
a₁+a₂ = 5

Row 2 - 1/9 · Row 1 → Row 2
9a₁-a₂ = 0
1.11a₂ = 5


a2 = 5/1.11111111 = 4.5
a1 = 0+a2/9 = 0+4.5/9 = 0.5

a₁ = 1/2 = 0.5
a₂ = 9/2 = 4.5

Our linear equations calculator calculates it.

$a_2=4.5=\frac{9}{2}\text{l}=4.5\text{l}$

$$\begin{gathered} b_1=2\text{l} \\ {b}_2=9\cdot b_1=9\cdot 2=18\text{l} \\ b=b_1+b_2=2+18=20\text{l} \end{gathered}$$

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