A cake recipe uses 150 g sugar in 400 g of flour. Find the ratio of: a. sugar to flour b. flour to sugar c. sugar to the amount of sugar and flour

Answer

To solve the problem step by step, we will find the required ratios based on the given quantities of sugar and flour.

### Given:
- Sugar = 150 g
- Flour = 400 g

### Step 1: Find the ratio of sugar to flour.
To find the ratio of sugar to flour, we can express it as:
\[ \text{Ratio of Sugar to Flour} = \frac{\text{Sugar}}{\text{Flour}} = \frac{150}{400} \]

**Simplifying the fraction:**
- We can divide both the numerator and the denominator by 50:
\[ \frac{150 \div 50}{400 \div 50} = \frac{3}{8} \]

**Final answer for part (a):**
\[ \text{Ratio of Sugar to Flour} = 3:8 \]

### Step 2: Find the ratio of flour to sugar.
To find the ratio of flour to sugar, we can express it as:
\[ \text{Ratio of Flour to Sugar} = \frac{\text{Flour}}{\text{Sugar}} = \frac{400}{150} \]

**Simplifying the fraction:**
- We can divide both the numerator and the denominator by 50:
\[ \frac{400 \div 50}{150 \div 50} = \frac{8}{3} \]

**Final answer for part (b):**
\[ \text{Ratio of Flour to Sugar} = 8:3 \]

### Step 3: Find the ratio of sugar to the total amount of sugar and flour.
First, we need to calculate the total amount of sugar and flour:
\[ \text{Total} = \text{Sugar} + \text{Flour} = 150 + 400 = 550 \]

Now, we can find the ratio of sugar to the total amount:
\[ \text{Ratio of Sugar to Total} = \frac{\text{Sugar}}{\text{Total}} = \frac{150}{550} \]

**Simplifying the fraction:**
- We can divide both the numerator and the denominator by 50:
\[ \frac{150 \div 50}{550 \div 50} = \frac{3}{11} \]

**Final answer for part (c):**
\[ \text{Ratio of Sugar to Total} = 3:11 \]

### Summary of Answers:
a. Ratio of Sugar to Flour = 3:8
b. Ratio of Flour to Sugar = 8:3
c. Ratio of Sugar to the Total Amount = 3:11