(4) $$ 20000: ?=1000: 1 $$ (5) $$ ?: 400=4: 100 $$ (7) $$ 7: 0,2=7: 6 $$, (8) $$ 8 \mathrm{~cm}: 1 \mathrm{~m}=?: 250 $$ (9) 20 seconds $$ : 2 $$ minutes $$ =1: $$ ? (10) $$ 30 \mathrm{~g}: ? \mathrm{mg}=40: 1 $$ (11) ? hours, 10 seconds $$ =720: 1 $$ Divide the number 720 into the following ratios: (1) $$ 5: 4 $$ (2) $$ 1: 9 $$ (3) $$ 2: 1: 3 $$ Divide each of the following numbers in a ratio of $$ 5: 3 $$ : (1) 80 (2) 176 (3) 100 Divide the following numbers in a ratio $$ 1: 5: 5 $$ : (1) (2) 33 (3) 253 The ratio- of boys to eirls at a party is $$ 4: 3 $$. If there are 20 boys, how many

Question

UpStudy AI · Accepted Answer

Sure, let's solve each of the ratio and proportion problems step by step.

---

### **Problem (4)**
$$ 20000 : \, ? \, = \, 1000 : 1 $$

**Solution:**
Set up the proportion:
$$
\frac{20000}{x} = \frac{1000}{1}
$$
Cross-multiply:
$$
20000 \times 1 = 1000 \times x \
20000 = 1000x \
x = \frac{20000}{1000} = 20
$$

**Answer:** **20**

---

### **Problem (5)**
$$ \, ? \, : \, 400 \, = \, 4 : 100 $$

**Solution:**
Set up the proportion:
$$
\frac{x}{400} = \frac{4}{100}
$$
Cross-multiply:
$$
100x = 4 \times 400 \
100x = 1600 \
x = \frac{1600}{100} = 16
$$

**Answer:** **16**

---

### **Problem (7)**
$$ 7 : 0.2 \, = \, 7 : 6 $$

**Solution:**
This appears to be an incomplete or incorrectly stated problem. If the intention is to find an equivalent ratio or to solve for a missing value, additional information is needed. Please provide more details or clarify the problem statement.

---

### **Problem (8)**
$$ 8 \, \text{cm} : 1 \, \text{m} = \, ? : 250 $$

**Solution:**
First, convert meters to centimeters:
$$
1 \, \text{m} = 100 \, \text{cm}
$$
Set up the proportion:
$$
\frac{8}{100} = \frac{x}{250}
$$
Solve for $$ x $$:
$$
x = \frac{8 \times 250}{100} = \frac{2000}{100} = 20
$$

**Answer:** **20**

---

### **Problem (9)**
$$ 20 \, \text{seconds} : 2 \, \text{minutes} = 1 : \, ? $$

**Solution:**
Convert minutes to seconds:
$$
2 \, \text{minutes} = 120 \, \text{seconds}
$$
Set up the proportion:
$$
\frac{20}{120} = \frac{1}{x}
$$
Solve for $$ x $$:
$$
x = \frac{120 \times 1}{20} = 6
$$

**Answer:** **6**

---

### **Problem (10)**
$$ 30 \, \text{g} : \, ? \, \text{mg} = 40 : 1 $$

**Solution:**
Convert grams to milligrams:
$$
30 \, \text{g} = 30000 \, \text{mg}
$$
Set up the proportion:
$$
\frac{30000}{x} = \frac{40}{1}
$$
Solve for $$ x $$:
$$
x = \frac{30000}{40} = 750
$$

**Answer:** **750 mg**

---

### **Problem (11)**
$$ \, ? \, \text{hours} : 10 \, \text{seconds} = 720 : 1 $$

**Solution:**
First, convert hours and seconds to the same unit. Let's convert hours to seconds:
$$
x \, \text{hours} = x \times 3600 \, \text{seconds}
$$
Set up the proportion:
$$
\frac{x \times 3600}{10} = \frac{720}{1}
$$
Solve for $$ x $$:
$$
x \times 3600 = 720 \times 10 \
x \times 3600 = 7200 \
x = \frac{7200}{3600} = 2
$$

**Answer:** **2 hours**

---

### **Dividing the Number 720 into Given Ratios**

#### **(1) Ratio $$ 5 : 4 $$**
- **Total parts:** $$ 5 + 4 = 9 $$
- **Each part:** $$ \frac{720}{9} = 80 $$
- **Division:** 
  - First part: $$ 5 \times 80 = 400 $$
  - Second part: $$ 4 \times 80 = 320 $$
  
**Answer:** **400 : 320**

#### **(2) Ratio $$ 1 : 9 $$**
- **Total parts:** $$ 1 + 9 = 10 $$
- **Each part:** $$ \frac{720}{10} = 72 $$
- **Division:**
  - First part: $$ 1 \times 72 = 72 $$
  - Second part: $$ 9 \times 72 = 648 $$
  
**Answer:** **72 : 648**

#### **(3) Ratio $$ 2 : 1 : 3 $$**
- **Total parts:** $$ 2 + 1 + 3 = 6 $$
- **Each part:** $$ \frac{720}{6} = 120 $$
- **Division:**
  - First part: $$ 2 \times 120 = 240 $$
  - Second part: $$ 1 \times 120 = 120 $$
  - Third part: $$ 3 \times 120 = 360 $$
  
**Answer:** **240 : 120 : 360**

---

### **Dividing Numbers in the Ratio $$ 5 : 3 $$**

#### **(1) Number 80**
- **Total parts:** $$ 5 + 3 = 8 $$
- **Each part:** $$ \frac{80}{8} = 10 $$
- **Division:**
  - First part: $$ 5 \times 10 = 50 $$
  - Second part: $$ 3 \times 10 = 30 $$
  
**Answer:** **50 : 30**

#### **(2) Number 176**
- **Total parts:** $$ 5 + 3 = 8 $$
- **Each part:** $$ \frac{176}{8} = 22 $$
- **Division:**
  - First part: $$ 5 \times 22 = 110 $$
  - Second part: $$ 3 \times 22 = 66 $$
  
**Answer:** **110 : 66**

#### **(3) Number 100**
- **Total parts:** $$ 5 + 3 = 8 $$
- **Each part:** $$ \frac{100}{8} = 12.5 $$
- **Division:**
  - First part: $$ 5 \times 12.5 = 62.5 $$
  - Second part: $$ 3 \times 12.5 = 37.5 $$
  
**Answer:** **62.5 : 37.5**

---

### **Dividing Numbers in the Ratio $$ 1 : 5 : 5 $$**

#### **(2) Number 33**
- **Total parts:** $$ 1 + 5 + 5 = 11 $$
- **Each part:** $$ \frac{33}{11} = 3 $$
- **Division:**
  - First part: $$ 1 \times 3 = 3 $$
  - Second part: $$ 5 \times 3 = 15 $$
  - Third part: $$ 5 \times 3 = 15 $$
  
**Answer:** **3 : 15 : 15**

#### **(3) Number 253**
- **Total parts:** $$ 1 + 5 + 5 = 11 $$
- **Each part:** $$ \frac{253}{11} = 23 $$
- **Division:**
  - First part: $$ 1 \times 23 = 23 $$
  - Second part: $$ 5 \times 23 = 115 $$
  - Third part: $$ 5 \times 23 = 115 $$
  
**Answer:** **23 : 115 : 115**

---

### **Final Problem**
**The ratio of boys to girls at a party is $$ 4 : 3 $$. If there are 20 boys, how many girls are there?**

**Solution:**
Given the ratio $$ 4 : 3 $$ (boys : girls), and there are 20 boys.

- **Each part for boys:** $$ \frac{20 \text{ boys}}{4} = 5 $$
- **Girls:** $$ 3 \times 5 = 15 $$

**Answer:** **15 girls**

---

If you have any further questions or need additional explanations, feel free to ask!
**Solutions:** 1. **Problem (4):** 20 2. **Problem (5):** 16 3. **Problem (7):** Cannot determine with given information. 4. **Problem (8):** 20 5. **Problem (9):** 6 6. **Problem (10):** 750 mg 7. **Problem (11):** 2 hours **Dividing 720 into Ratios:** 1. **5 : 4** → 400 : 320 2. **1 : 9** → 72 : 648 3. **2 : 1 : 3** → 240 : 120 : 360 **Dividing Numbers in the Ratio 5 : 3:** 1. **80** → 50 : 30 2. **176** → 110 : 66 3. **100** → 62.5 : 37.5 **Dividing Numbers in the Ratio 1 : 5 : 5:** 1. **33** → 3 : 15 : 15 2. **253** → 23 : 115 : 115 **Final Problem:** There are 15 girls at the party. If you have more questions or need further assistance, feel free to ask!

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