Question

the royal family company produces two types of drink. The first type is 35% pure fruit juice,and the second type is 85% pure fruit juice.company is attempting to produce a fruit drink that contains 70% fruit juice.how many pints of each of the two existing types of drink must be used to make 30 pints of a mixture that is 70% pure fruit juice?first fruit drink :___second fruit drink:___

Answer 1

The amount of pint of the first drink type is;

`9\text{ pints}`

The amount of pint of the second drink type is;

`21\text{ pints}`

Step-by-step explanation:

Let x represent the amount of pint of the first type

The amount of the second type will be;

`30-x`

Since the total amount of the mixture is 30 pint.

Equating the amount of pure fruit in each type to that of the mixture.

`\begin{gathered} \text{first type = 35\% =0.35} \\ \text{second type = 85\% = 0.85} \\ \text{Mixture = 70\% = 0.70} \end{gathered}`

We have;

`0.35(x)+0.85(30-x)=0.70(30)`

solving for x;

`\begin{gathered} 0.35(x)+0.85(30)-0.85(x)=0.70(30) \\ 0.35x-0.85x+25.5=21 \\ -0.50x=21-25.5 \\ -0.50x=-4.5 \\ (-0.50x)/(-0.50)=(-4.5)/(-0.50) \\ x=9 \end{gathered}`

The amount of pint of the first type is;

`9\text{ pints}`

So, the amount of pint of the second type will be;

`\begin{gathered} 30-x=30-9 \\ =21 \end{gathered}`

The amount of pint of the second type is;

`21\text{ pints}`