At a construction site, cement, sand, and gravel are mixed to make concrete. The ratio of cement to sand to gravel is 1 to 2.4 to 3.6. If a 150-lb bag of sand is used, how much cement and gravel must be used?

The given ratio of cement to sand to gravel is 1:2.4:3.6. If 150 pounds of sand are used, we need to determine how much cement and gravel are needed to maintain this ratio.

### Step 1: Express the ratio in terms of a common factor
Let the common factor be \( x \). The amounts of cement, sand, and gravel can be expressed as:
- Cement = \( 1x \)
- Sand = \( 2.4x \)
- Gravel = \( 3.6x \)

We know that the amount of sand is 150 pounds, so:
\[
2.4x = 150
\]

### Step 2: Solve for \( x \)
To find \( x \), divide both sides of the equation by 2.4:
\[
x = \frac{150}{2.4} = 62.5
\]

### Step 3: Calculate the amounts of cement and gravel
Now that we know \( x = 62.5 \), we can calculate the amounts of cement and gravel.

- Cement: \( 1x = 1 \times 62.5 = 62.5 \) pounds
- Gravel: \( 3.6x = 3.6 \times 62.5 = 225 \) pounds

### Final Answer:
To maintain the given ratio, if 150 pounds of sand are used, you would need:
- 62.5 pounds of cement
- 225 pounds of gravel

Would you like a detailed explanation of any part of the solution?

Here are 5 related questions to explore:
1. If the ratio of cement to sand changes, how does that affect the amount of gravel used?
2. What is the total weight of the mixture of cement, sand, and gravel?
3. How would the solution change if the weight of sand was 100 pounds instead of 150?
4. How do ratios impact mixtures in construction settings?
5. Can you find the percentage of each material in the final concrete mix?

**Tip**: Always reduce ratios to their simplest form to easily work with proportions.

Learn how to calculate the amounts of cement and gravel required when mixing concrete using a 1:2.4:3.6 ratio with 150 lbs of sand. This step-by-step guide covers essential math concepts like ratios, proportions, and basic algebra. Ideal for students in Grades 6-8.

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