SOLUTION: The Royal Fruit Company produces two types of fruit drinks. The first type is 20% pure fruit juice, and the second type is 70% pure fruit juice. The company is attempting to produc

Question 1203315: The Royal Fruit Company produces two types of fruit drinks. The first type is 20% pure fruit juice, and the second type is 70% pure fruit juice. The company is attempting to produce a fruit drink that contains 35% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 35% pure fruit juice?
Found 4 solutions by math_tutor2020, ikleyn, josgarithmetic, greenestamps:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Answers:
35 pints of the 20% drink
15 pints of the 70% drink

Work Shown

x = amount of the 20% juice (1st batch)
50-x = amount of the 70% juice (2nd batch)
Each amount is in pints.
These two expressions add to 50 pints total.

0.2x = amount of pure fruit from the 1st batch
0.7(50-x) = 35-0.7x = amount of pure fruit from the 2nd batch

batch1+batch2 = (0.2x) + (35-0.7x) = 35-0.5x = total amount of pure fruit

The goal is to make a 35% fruit drink, and the company wants 50 pints.
Therefore, the company requires 0.35*50 = 17.5 pints of pure fruit.
This leads us to the equation
35-0.5x = 17.5

Let's solve for x
35-0.5x = 17.5
-0.5x = 17.5-35
-0.5x = -17.5
x = -17.5/(-0.5)
x = 35
We'll need 35 pints of the 20% batch.

Also we'll need 15 pints of the 70% batch because 50-x = 50-35 = 15.

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
The Royal Fruit Company produces two types of fruit drinks.
The first type is 20% pure fruit juice, and the second type is 70% pure fruit juice.
The company is attempting to produce a fruit drink that contains 35% pure fruit juice.
How many pints of each of the two existing types of drink must be used to make
50 pints of a mixture that is 35% pure fruit juice?
~~~~~~~~~~~~~~~

x pints of the 70% juice, and (50-x) pints of the 20% juice. x pints of the 70% juice contain 0.7x pints of the pure juice; (50-x) pints of the 20% juice contain 0.2(50-x) pints of the pure juice. 50 pints of the final mixture contain 0.35*50 pints of the pure juice. When we chose this presentation of ingredients, x and (50-x) pints, we just provided the total volume of the mixture of x + (50-x) = 50 pints. The only condition which remained and which we should satisfy was to make a balance of the pure juice in ingredients and in the final mixture. So, we write this equation for the pure juice amounts 0.7x + 0.2*(50-x) = 0.35*50 pints of the pure juice. Simplify the equation and find x 0.7x + 10 - 0.2x = 17.5 0.7x - 0.2x = 17.5 - 10 0.5x = 7.5 x = 7.5/0.5 = 15 pints. ANSWER. 15 pints of the 70% juice and (50-15) = 35 pints of the 20% juice.

Solved.

------------------

It is a standard and typical mixture problem.

For introductory lessons covering various types of mixture word problems see
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Typical word problems on mixtures from the archive
in this site.

You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization, from very detailed to very short.

Read them and become an expert in solution mixture word problems.

Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!
Another mixture problem for Royal Fruit Company

TYPE %PureJuice VOL. AMT. PURE first 20 50-d 0.2(50-d) second 70 d 0.7d Mixture 35 50 0.35*50

This makes sense, yes?
You see accounting for amount of pure juice?

and hold off on the computations until the end.
.
.
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

Here is a fast and easy informal way to solve any 2-part mixture problem like this, if formal algebra is not required.

Observe/calculate that 35% is 15/50 = 3/10 of the way from 20% to 70%.
That means 3/10 of the mixture is the ingredient with the higher percentage of fruit juice.

ANSWERS:
3/10 of 50 pints, or 15 pints, of the drink with 70% fruit juice; the other 50-15 = 35 pints of the drink with 20% fruit juice.

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