Question

A beverage producer makes two products, Pi Cola, containing 10% cola, and Pi Up, containing 50% cola. How many gallons of Pi Up must be mixed with 300 gallons of Pi Cola to create a new product containing 40% cola?

Answer 1

Answer:

The number of gallons of Pi Up required is 900 gallons.

Step-by-step explanation:

Two different drinks that are produced by the beverage producer are Pi Cola which contains 10% Cola and Pi Up which contains 50% cola.

A solution is to be created using Pi Cola and Pi Up to create a new product containing 40% cola.

It has been mentioned that the number of gallons of Pi Up to be used is 300 gallons.

We can write that the number of gallons of Pi Up that must be mixed with 300 gallons of Pi Cola be x gallons.

So we write the first equation and we can say that the total number of gallons of the solution is x + 300.

Equating the percentage of cola from each beverage to get the required 40% cola we can write

  (0.1 × 300) + (0.5 × x)  = 0.4 × ( x + 300)

If we solve for x from the above equation we get

  (0.5 x + 30)  = (0.4 x + 120)

⇒ 0.1 x  = (120 - 30)  = 90

⇒ x  = 900 gallons

Therefore the number of gallons of Pi Up required is 900.