Question

help!!!!!!!!!!!!!!!!!! A soap maker uses a mixture of 3 kg of natural animal fat and 5 kg of synthetic fat to create his soap. In order to make 512 kg of his soap, how many kg of synthetic fat are needed?
320
192
307
819
853

Answer 1

Number of kilograms of natural animal fat used = 3 kg.

Number of kilograms of synthetic fat used = 5 kg.

The ratio of natural animal fat used to synthetic fat used = 3:5.

Let us assume number kilograms of natural animal fat used to make 512 kg of soap. = x kg.

And number of kilograms used for synthetic fat would be (512-x) kg.

Now, we can setup a proportion.

$\frac{x}{512-x}=\frac{3}{5}$

On cross multiplying, we get

5*x = 3*(512-x).

5x = 1536 -3x.

Adding 3x on both sides, we get

5x+3x = 1536 -3x+3x.

8x = 1536.

Dividing both sides by 8, we get

8x/8= 1536/8

x=192.

But we took x for number kilograms of natural animal fat used.

And we have

Number of kilograms used for synthetic fat = 512-192 = 320 kg.

Therefore, number of kilograms used for synthetic fat = 320kg.

First option is correct.