Question

Kimo Leahi works at the Juice Joint. He adds 7 liters of orange juice to guava juice to make a mixture of guava-orange juice. A liter of orange juice sells for $2, and a liter of guava juice sells for $3. If a liter of guava-orange juice is to sell for $2.65, how many liters of guava juice should Kimo start with?

Answer 1

Take a basis of 1 liter and let x be the fraction of volume in that 1 liter that orange juice occupies. Then the guava juice will consist of (1-x) of the volume. For your concoction, one liter will cost\[$2x+$3(1-x)=$2.65\]Solving for x\[x=0.35\]That is, 35% of the volume will be orange juice, which means 65% will be guava juice. Since you know 35% of the total volume is orange juice,\[7L = 0.35V \rightarrow V=\frac{7L}{0.35}=20L\]which means the volume of guava juice is\[0.65V=0.65 \times 20L = 13L\]If you test this, your 20 liters of juice would cost\[13 \times $3+7 \times $2=$53\]that is,\[\frac{$53}{20L}=$2.65 /L\]