In a game of 200 points, A can give 40 points to B and 56 points to C How many points can B give to C?

Options

A. 20 points
B. 15 points
C. 10 points
D. 5 points

Answer

To solve the problem step by step, we will analyze the points given in the game and use ratios to find out how many points B can give to C.

### Step 1: Understand the Points Distribution
A can give 40 points to B and 56 points to C in a game of 200 points. This means:
- A has 200 points initially.
- After giving 40 points to B, A has \(200 - 40 = 160\) points left.
- After giving 56 points to C, A has \(200 - 56 = 144\) points left.

### Step 2: Set Up Ratios
We can set up the following ratios based on the points after A gives points to B and C:
- Points of A after giving to B: 160
- Points of A after giving to C: 144

Now, we can set up the ratios:
- A : B = 200 : 160
- A : C = 200 : 144

### Step 3: Find the Ratio of B to C
Using the ratios, we can find the ratio of B to C:
\[ \frac{B}{C} = \frac{B}{A} \times \frac{A}{C} \]
Substituting the values:
\[ \frac{B}{C} = \frac{160}{200} \times \frac{200}{144} \]

### Step 4: Simplify the Ratios
Now we will simplify the expression:
1. The \(200\) in the numerator and denominator cancels out:
\[ \frac{B}{C} = \frac{160}{144} \]
2. Simplifying \( \frac{160}{144} \):
- Divide both numerator and denominator by 16:
\[ \frac{B}{C} = \frac{10}{9} \]

### Step 5: Calculate Points B Can Give to C
Now, if B has 200 points (the same as A), we can find out how many points B can give to C:
- If B has 10 parts, C has 9 parts. The total parts = 10 + 9 = 19 parts.
- Each part represents \( \frac{200}{19} \) points.

Now we calculate how many points B can give to C:
- B's points = \( \frac{10}{19} \times 200 = \frac{2000}{19} \approx 105.26 \) points.
- C's points = \( \frac{9}{19} \times 200 = \frac{1800}{19} \approx 94.74 \) points.

### Step 6: Final Calculation
To find how many points B can give to C:
- The difference between B's and C's points:
\[ B - C = 105.26 - 94.74 = 10.52 \approx 10 \text{ points} \]

Thus, B can give approximately **10 points** to C.

### Summary of the Solution
B can give **10 points** to C.