1. Let's assume the number of boys in the first grade is x. According to the given information, the number of girls would be x + 26, as there are 26 more girls than boys.
So, the total number of students in the first grade would be x (boys) + x + 26 (girls) = 364.
Combining like terms, we have 2x + 26 = 364.
Subtracting 26 from both sides, we get 2x = 338.
Finally, dividing both sides by 2, we find x = 169.
Therefore, there are 169 boys and 169 + 26 = 195 girls in the first grade.
2. Let's assume the height of the taller ladder is x feet. According to the given information, the height of the shorter ladder would be x - 6.5 feet.
The combined height of the two ladders is 31.5 feet, so we can write it as:
x + (x - 6.5) = 31.5
Combining like terms, we have 2x - 6.5 = 31.5.
Adding 6.5 to both sides, we get 2x = 38.
Finally, dividing both sides by 2, we find x = 19.
Therefore, the height of the taller ladder is 19 feet, and the height of the shorter ladder is 19 - 6.5 = 12.5 feet.
