Question

A mixture weighing 600kg has two ingredients: sand, cement and stones. There is twice as much cement as sand and three times as much stones as sand. How much cement in the mixture?

Answer 1

Explanation:

All the masses here are based on the main mass of the sand. So we will call sand "x". If there is two times as much cement as sand, then cement is 2x; if there is three times as much stone as sand, then stone is 3x. All of these added together equal a mass of 600 kg:

x + 2x + 3x = 600 so

6x = 600 and

x = 100 kg

There are 100 kg of sand. That means that there is 200 kg of cement and 300 kg of stone

Answer 2

200 kg

Explanation:

Total weight of the mixture = 600kg

Let the weight of the cement in the mixture be x kg.

According to the problem statement, there is twice as much cement as sand, therefore the weight of sand relative to cement will be 1/2, i.e.

sand weight = 1/2x =0.5x

Similarly, weight of stone will be three times as much as sand.

Meaning, stone weight = 3*0.5x=1.5x

Total weight of all the components will be

cement weight + sand weight + stone weight =

x + 0.5x + 1.5x = 3x

But 3x = 600,

x = 600/3= 200 kg