Question

A candy distributor needs to mix a 30% fat-content chocolate with a 40% fat-content chocolate to create 150 kilograms of a 32% fat-content chocolate. How many kilograms of each kind of chocolate must they use?

Answer 1

120 kg of 30% fat-content chocolate and 30 kg of 40% fat-content chocolate.

Explanation:

We are given that a candy distributor needs to mix a 30% fat-content chocolate with a 40% fat-content chocolate to create 150 kilograms of a 32% fat-content chocolate.

Let the amount of 30% fat-content chocolate be 'x' and the amount of 40% fat-content chocolate be 'y'.

So, according to the question;

x + y = 150 ------------ [equation 1]

and
`30\% \text{ of } x + 40\% \text{ of } y=32\% \text{ of } 150`

`30x+40y= 32 * 150`

`30x+40* (150-x)= 4800`

`30x+6000-40x= 4800`

`10x = 6000-4800`

`x=(1200)/(10)`

x = 120 kg

Now, putting the value of x in equation 1, we get;

x + y = 150

120 + y = 150

y = 30 kg

Hence, 120 kg of 30% fat-content chocolate and 30 kg of 40% fat-content chocolate.