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.
Now, we can set up an equation to represent the problem:
x + (x + 26) = 362
Combining like terms, we have:
2x + 26 = 362
Subtracting 26 from both sides of the equation:
2x = 362 - 26
2x = 336
Dividing both sides by 2:
x = 336 / 2
x = 168
So, there are 168 boys in the first grade. To find the number of girls, we can substitute this value back into our equation:
x + 26 = 168 + 26
x + 26 = 194
Therefore, there are 194 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 other ladder would be x - 6.5 feet.
We can set up an equation to represent the problem:
x + (x - 6.5) = 31.5
Combining like terms, we have:
2x - 6.5 = 31.5
Adding 6.5 to both sides of the equation:
2x = 31.5 + 6.5
2x = 38
Dividing both sides by 2:
x = 38 / 2
x = 19
So, the height of the taller ladder is 19 feet. To find the height of the other ladder, we can substitute this value back into our equation:
x - 6.5 = 19 - 6.5
x - 6.5 = 12.5
Therefore, the height of the other ladder is 12.5 feet.
