The initial ratio of sugar and flour in a dough was 4:7. With 22 kg of the dough Justine added more flour to make the sugar to flour ratio 2:5. How much flour did Justine later add?

Options

A. 4 kg
B. 6 kg
C. 8 kg
D. 2 kg

Answer

To solve the problem step by step, we will follow the given information and calculate how much flour Justine added to the dough.

### Step 1: Understand the initial ratio of sugar to flour
The initial ratio of sugar to flour in the dough is given as 4:7. This means for every 4 parts of sugar, there are 7 parts of flour.

### Step 2: Set up the equations based on the initial ratio
Let the common factor be \( x \). Therefore:
- Amount of sugar = \( 4x \)
- Amount of flour = \( 7x \)

The total amount of dough is given as 22 kg:
\[ 4x + 7x = 22 \]
\[ 11x = 22 \]
\[ x = 2 \]

### Step 3: Calculate the initial quantities of sugar and flour
Now, substituting \( x \) back into the equations:
- Amount of sugar = \( 4x = 4 \times 2 = 8 \) kg
- Amount of flour = \( 7x = 7 \times 2 = 14 \) kg

### Step 4: Set up the new ratio after adding flour
Justine adds \( y \) kg of flour to the dough, and the new ratio of sugar to flour becomes 2:5. The amount of sugar remains the same (8 kg), and the new amount of flour is \( 14 + y \) kg.

### Step 5: Set up the equation for the new ratio
According to the new ratio:
\[ \frac{8}{14 + y} = \frac{2}{5} \]

### Step 6: Cross-multiply to solve for \( y \)
Cross-multiplying gives:
\[ 8 \times 5 = 2 \times (14 + y) \]
\[ 40 = 28 + 2y \]

### Step 7: Solve for \( y \)
Now, isolate \( y \):
\[ 40 - 28 = 2y \]
\[ 12 = 2y \]
\[ y = 6 \]

### Conclusion
Justine added **6 kg** of flour to the dough.

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