(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!

Upstudy AI Solution

Answer

Solution

Problem (4)

Problem (5)

Problem (7)

Problem (8)

Problem (9)

Problem (10)

Problem (11)

Dividing the Number 720 into Given Ratios

(1) Ratio

(2) Ratio

(3) Ratio

Dividing Numbers in the Ratio

(1) Number 80

(2) Number 176

(3) Number 100

Dividing Numbers in the Ratio

(2) Number 33

(3) Number 253

Final Problem

Bonus Knowledge

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