What is the ratio of students taken for all years together from school B to that from from school A?

Options

A. `370:429`
B. `415:401`
C. 429:370
D. 401:415

Answer

To find the ratio of students taken for all years together from school B to that from school A, we will follow these steps:

### Step 1: Calculate the total number of students from School A
We need to sum the number of students from School A over the 6 years. The numbers are:
- Year 1: 640
- Year 2: 800
- Year 3: 500
- Year 4: 700
- Year 5: 900
- Year 6: 750

**Calculation:**
\[ \text{Total from School A} = 640 + 800 + 500 + 700 + 900 + 750 \]
\[ = 640 + 800 = 1440 \]
\[ = 1440 + 500 = 1940 \]
\[ = 1940 + 700 = 2640 \]
\[ = 2640 + 900 = 3540 \]
\[ = 3540 + 750 = 4290 \]

**Total from School A = 4290**

### Step 2: Calculate the total number of students from School B
Now we will sum the number of students from School B over the 6 years. The numbers are:
- Year 1: 550
- Year 2: 820
- Year 3: 600
- Year 4: 750
- Year 5: 500
- Year 6: 480

**Calculation:**
\[ \text{Total from School B} = 550 + 820 + 600 + 750 + 500 + 480 \]
\[ = 550 + 820 = 1370 \]
\[ = 1370 + 600 = 1970 \]
\[ = 1970 + 750 = 2720 \]
\[ = 2720 + 500 = 3220 \]
\[ = 3220 + 480 = 3700 \]

**Total from School B = 3700**

### Step 3: Find the ratio of students from School B to School A
Now we will find the ratio of the total number of students from School B to the total number of students from School A.

**Calculation:**
\[ \text{Ratio} = \frac{\text{Total from School B}}{\text{Total from School A}} = \frac{3700}{4290} \]

### Step 4: Simplify the ratio
To simplify the ratio, we can divide both numbers by their greatest common divisor (GCD). In this case, we can cancel the common zeroes first.

\[ \frac{3700}{4290} = \frac{370}{429} \]

This fraction cannot be simplified further since 370 and 429 do not have any common factors other than 1.

### Final Answer
The ratio of students taken for all years together from School B to that from School A is **370:429**.

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