Using multiple strategies, we find that the expected number of boys in the class is around a) 264 (using a table), b) 160 (using ratio), c) 266 (using algebra).
To determine the number of boys in the class, we can use different strategies at different levels. Let's go through each level step by step:
a) Level 1: Using a table
We can create a table to organize the information given. Since there are 12 girls for every 8 boys, we can assume that the total number of students is divided into 12 equal groups (girls) and 8 equal groups (boys).
| | Girls | Boys |
| --- | ----- | ---- |
| 1 | 12 | 8 |
| 2 | 24 | 16 |
| 3 | 36 | 24 |
| ... | ... | ... |
| 12 | 144 | 96 |
From the table, we can see that for every group of 12 girls, there are 8 boys. So, if there are 400 students in total, we can divide 400 by 12 to find out how many groups of girls there are.
400 ÷ 12 = 33 R 4
This means that there are 33 groups of girls with 4 students left over. Each group of girls has 8 boys, so we can multiply 33 by 8 to find the total number of boys.
33 × 8 = 264
Therefore, we can expect there to be 264 boys in the class.
b) Level 2: Using ratio
We know that the ratio of girls to boys is 12:8. This ratio can be simplified to 3:2 by dividing both numbers by their greatest common divisor, which is 4.
To find the number of boys, we can use the fact that the total number of students is 400. The total ratio is 3+2=5 (3 parts for girls and 2 parts for boys).
So, the number of boys can be found by multiplying the total number of students by the fraction representing the boys' part in the ratio:
400 × (2/5) = 160
Therefore, we can expect there to be 160 boys in the class.
c) Level 3: Using algebra
Let's use algebra to solve this problem.
Let's assume the number of boys in the class is x.
The number of girls can be calculated using the ratio of 12 girls for 8 boys, which simplifies to 3:2. We can set up the following equation:
(3/2)x = 400
To solve for x, we can multiply both sides of the equation by 2/3:
x = (2/3) × 400
x = 800/3
x ≈ 266.67
Since we can't have a fraction of a student, we can round down to the nearest whole number. Therefore, we can expect there to be 266 boys in the class.
Overall, using multiple strategies, we find that the expected number of boys in the class is around 264 (using a table), 160 (using ratio), or 266 (using algebra).