# The concentration of cheaper brand in the punch.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.6, Problem 59E
To determine

## To find: The concentration of cheaper brand in the punch.

Expert Solution

The concentration of cheaper brand is 35% in the punch.

### Explanation of Solution

Given:

The concentration of fruit juice is 50% in a bottle of 750 ml fruit punch.

Jill drinks 100 ml of fruit punch and refills the bottle with equal amount of cheaper brand of punch.

The concentration of juice now in bottle is 48%.

Calculation:

Let the concentration of cheaper brand be x.

Tabulate the given information into the language of algebra.

 In words In Algebra Concentration of cheaper brand x Amount of fruit juice before refill 0.50(750−100) 48% of concentration of juice 0.48(750)

Model the equation for the above information.

(Amountjuicefromcheaperbrand)+(Amountofjuicebeforerefill)=48%ofconcentrartion100x+0.50(750100)=0.48(750)

Simplify the above equation for x,

100x+0.50(100)=360100x+325=360100x=35x=35%

Thus, the concentration of cheaper brand is 35% in the punch.

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