A mixture of iron, sand, and glass contains the three ingredients in the ratio `"4:7:9"`, respectively. How much and what percentage of iron, sand, and glass is in 500 g of the mixture?

Answer

To solve the problem step by step, we need to determine the amounts and percentages of iron, sand, and glass in a 500 g mixture based on the given ratio of 4:7:9.

### Step 1: Understand the Ratio
The ratio of iron, sand, and glass is given as 4:7:9. This means:
- Iron = 4 parts
- Sand = 7 parts
- Glass = 9 parts

### Step 2: Calculate Total Parts
To find the total number of parts in the mixture, we add the parts of each ingredient:
\[ \text{Total parts} = 4 + 7 + 9 = 20 \]

### Step 3: Calculate the Weight of Each Ingredient
Now, we will calculate the weight of each ingredient in the 500 g mixture.

#### Iron:
Using the ratio for iron:
\[ \text{Weight of Iron} = \left( \frac{4}{20} \right) \times 500 \]
Calculating this:
\[ \text{Weight of Iron} = \frac{4 \times 500}{20} = \frac{2000}{20} = 100 \text{ g} \]

#### Sand:
Using the ratio for sand:
\[ \text{Weight of Sand} = \left( \frac{7}{20} \right) \times 500 \]
Calculating this:
\[ \text{Weight of Sand} = \frac{7 \times 500}{20} = \frac{3500}{20} = 175 \text{ g} \]

#### Glass:
Using the ratio for glass:
\[ \text{Weight of Glass} = \left( \frac{9}{20} \right) \times 500 \]
Calculating this:
\[ \text{Weight of Glass} = \frac{9 \times 500}{20} = \frac{4500}{20} = 225 \text{ g} \]

### Step 4: Summary of Weights
Now we summarize the weights of each ingredient:
- Iron: 100 g
- Sand: 175 g
- Glass: 225 g

### Step 5: Calculate the Percentages
Next, we will calculate the percentage of each ingredient in the mixture.

#### Percentage of Iron:
\[ \text{Percentage of Iron} = \left( \frac{100}{500} \right) \times 100 = 20\% \]

#### Percentage of Sand:
\[ \text{Percentage of Sand} = \left( \frac{175}{500} \right) \times 100 = 35\% \]

#### Percentage of Glass:
\[ \text{Percentage of Glass} = \left( \frac{225}{500} \right) \times 100 = 45\% \]

### Final Summary
- Weight of Iron: 100 g (20%)
- Weight of Sand: 175 g (35%)
- Weight of Glass: 225 g (45%)