In a library, the ratio of the number of mathematics books to that of physics books, is the same as the ratio of the number of the physics books to that of chemistry books. If there are 144 mathematics books and 100 chemistry books, then the ratio of the total number of mathematics and physics books to the total number of chemistry and physics books is:

Options

A. `3:2`
B. `6:5`
C. `5:4`
D. `4:3`

Answer

To solve the problem, we need to establish the relationships between the number of mathematics, physics, and chemistry books based on the given information.

### Step-by-Step Solution:

1. **Define Variables**:
Let:
- \( M \) = number of mathematics books = 144
- \( P \) = number of physics books
- \( C \) = number of chemistry books = 100

2. **Set Up Ratios**:
According to the problem, the ratio of mathematics books to physics books is the same as the ratio of physics books to chemistry books. This can be expressed mathematically as:
\[ \frac{M}{P} = \frac{P}{C} \]

3. **Substitute Known Values**:
Substitute the known values of \( M \) and \( C \) into the ratio:
\[ \frac{144}{P} = \frac{P}{100} \]

4. **Cross Multiply**:
To eliminate the fractions, we cross-multiply:
\[ 144 \times 100 = P \times P \]
This simplifies to:
\[ 14400 = P^2 \]

5. **Solve for \( P \)**:
Taking the square root of both sides gives:
\[ P = \sqrt{14400} = 120 \]

6. **Calculate Total Books**:
Now we can find the total number of mathematics and physics books, and the total number of chemistry and physics books:
- Total Mathematics and Physics books = \( M + P = 144 + 120 = 264 \)
- Total Chemistry and Physics books = \( C + P = 100 + 120 = 220 \)

7. **Find the Required Ratio**:
Now we can find the ratio of the total number of mathematics and physics books to the total number of chemistry and physics books:
\[ \text{Ratio} = \frac{M + P}{C + P} = \frac{264}{220} \]

8. **Simplify the Ratio**:
To simplify \( \frac{264}{220} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 44:
\[ \frac{264 \div 44}{220 \div 44} = \frac{6}{5} \]

### Final Answer:
The ratio of the total number of mathematics and physics books to the total number of chemistry and physics books is \( \frac{6}{5} \).