Answer to Question #136523 in Algebra for Faith

Question

Mrs mashiyu is building a rondavel for herself.she makes concrete for the foundation by mixing gravel,sand and cement in the ratio 5:3:2 by volume.
1. Calculate the amount of sand and cement that Mrs mashiyu needs to make of 20m3m3 concrete.
2. Show that your calculations are correct in three different ways.

Answer 1

We work out the total number of parts into which the concrete is divided: 5 + 3 + 2 = 10 parts altogether. Using the numbers in the ratio, we know then that gravel makes up 5 parts, sand 3 parts, and cement 2 parts. So there are 10 parts altogether, and we have 20 m³ of concrete, and therefore 1 part must equal 2 m³. Then as there are 3 parts of sand, the volume of sand needed must be 3 × 2 m³ which is 6 m³. Then as there are 2 parts of cement, the volume of cement needed must be 2 × 2 m³ which is 4 m³.

We now need to check the answer.

1. Sand and cement represent 5 parts out of a total of 10, in other words a half. So half of the total volume of concrete is sand and cement, and that is half of 20 m³, which is 10 m³. So that is indeed the correct answer.

2. Cement represents 2 parts out of a total of 10, in other words a 1/5. So 1/5 of the total volume of concrete is cement, and that is 1/5 of 20 m³, which is 4 m³. So that is indeed the correct answer.

3. Sand represents 3 parts out of a total of 10, in other words a 3/10. So 3/10 of the total volume of concrete is sand, and that is 3/10 of 20 m³, which is 6 m³. So that is indeed the correct answer.