Answer :
To find out how much sand Bob needs to make the 560 kg of concrete mix, we need to use the given ratio of cement, sand, and gravel, which is [tex]\(1:3:4\)[/tex].
Here's a step-by-step solution:
1. Understand the Ratio:
- The ratio [tex]\(1:3:4\)[/tex] means for every 1 part of cement, there are 3 parts of sand and 4 parts of gravel.
- Total parts in the ratio = [tex]\(1 + 3 + 4 = 8\)[/tex].
2. Calculate the Weight of Each Part:
- Since the total concrete mix weighs 560 kg, each part of the mix would contribute a portion of the total weight.
3. Determine the Weight of Sand:
- Sand is represented by 3 parts in the ratio.
- The weight of sand can be calculated by distributing the total weight according to the ratio:
[tex]\[
\text{Weight of sand} = \left(\frac{\text{Parts for sand}}{\text{Total parts}}\right) \times \text{Total weight of concrete mix}
\][/tex]
[tex]\[
\text{Weight of sand} = \left(\frac{3}{8}\right) \times 560 = 210 \text{ kg}
\][/tex]
Therefore, Bob needs 210 kg of sand for his concrete mix.
Here's a step-by-step solution:
1. Understand the Ratio:
- The ratio [tex]\(1:3:4\)[/tex] means for every 1 part of cement, there are 3 parts of sand and 4 parts of gravel.
- Total parts in the ratio = [tex]\(1 + 3 + 4 = 8\)[/tex].
2. Calculate the Weight of Each Part:
- Since the total concrete mix weighs 560 kg, each part of the mix would contribute a portion of the total weight.
3. Determine the Weight of Sand:
- Sand is represented by 3 parts in the ratio.
- The weight of sand can be calculated by distributing the total weight according to the ratio:
[tex]\[
\text{Weight of sand} = \left(\frac{\text{Parts for sand}}{\text{Total parts}}\right) \times \text{Total weight of concrete mix}
\][/tex]
[tex]\[
\text{Weight of sand} = \left(\frac{3}{8}\right) \times 560 = 210 \text{ kg}
\][/tex]
Therefore, Bob needs 210 kg of sand for his concrete mix.
