Question

[Help Needed] Julie is mixing orange juice. She adds water to the concentrate until she has 2 liters of juice which is 60% concentrate. She then adds some leftover juice which is 75% concentrate. If the result is 65% concentrated juice, how many liters of the stronger mix did she add?

Answer 1

1 liter of the Stronger mix

Explanation:

From the above question:

Julie adds water to the concentrate until she has 2 liters of juice which is 60% concentrate.

Hence,

2 liters of juice = 60% concentrate of orange

2 liters of juice = 0.6 of the concentrate of orange

Amount of orange used in liters = 2 × 0.6 = 1.2 liters

She then adds some leftover juice which is 75% concentrate

Liters of left over juice added = unknown and represented by y

hence,

y liters of juice = 75% concentrate

y liters = 0.75 concentrate.

Liters of y added = y × 0.75

= 0.75y

She then adds some leftover juice which is 75% concentrate. If the result is 65% concentrated juice,

Mathematically this means

60% concentrate + 75 % concentrate = 65% concentrate.

In liters

= 1.2 liters + 0.75y liters = 65%(2 liters of orange + y liters of orange)

= 1.2 + 0.75y = 0.65(2 + y)

= 1.2 + 0.75y = 1.3 + 0.65y

Collect like terms

= 0.75y - 0.65y = 1.3 - 1.2

= 0.1y = 0.1

y = 0.1/0.1

y = 1 liter.

Hence, since the liters of the leftover juice = stronger mix is represented by y,

therefore, the liters of stronger mix added = 1 liter.