A 50 foot see-saw has 4 kids sitting on it. A 62 lb. girl sits on the left end, with a 76 lb. girl sitting 2.5 feet in front of her. On the right side, a 96 lb. boy sits on the end and has another boy sitting 2.5 feet in front of him. How much does this other boy weigh?

Question

A 50 foot see-saw has 4 kids sitting on it. A 62 lb. girl sits on the left end, with a 76 lb. girl sitting 2.5 feet in front of her. On the right side, a 96 lb. boy sits on the end and has another boy sitting 2.5 feet in front of him. How much does this other boy weigh?

Answer 1

balance the torques.

62(25) + 76(25-2) = 96(25) + x(25-2.5)

Now just solve for x

Answer 2

To find out the weight of the other boy, let's analyze the situation using the principle of moments or torque.

The moment of an object is the product of its weight and its distance from a reference point. In this case, the reference point can be chosen as the fulcrum or center of the seesaw.

Let's label the distances:
- The distance from the left end to the fulcrum is 25 feet.
- The distance from the right end to the fulcrum is also 25 feet.
- The distance between the girl and the boy on the same side is 2.5 feet.

Now let's calculate the moments about the fulcrum.

For the left side:
Moment of the 62 lb. girl = 62 lb. × (25 ft. - 2.5 ft.)
Moment of the 76 lb. girl = 76 lb. × (25 ft. - 5 ft.) [2.5 ft. added twice]
Total moment on the left side = Moment of the 62 lb. girl + Moment of the 76 lb. girl

For the right side:
Moment of the 96 lb. boy = 96 lb. × (25 ft. - 2.5 ft.)
Total moment on the right side = Moment of the 96 lb. boy + Moment of the other boy

According to the principle of moments, the total moment on the left side should be equal to the total moment on the right side.

So, to find out the weight of the other boy, we need to set up an equation:

Total moment on the left side = Total moment on the right side
(Moment of the 62 lb. girl + Moment of the 76 lb. girl) = (Moment of the 96 lb. boy + Moment of the other boy)

Now we can solve this equation to find the weight of the other boy. Let's do that:

62 lb. × (25 ft. - 2.5 ft.) + 76 lb. × (25 ft. - 5 ft.) = 96 lb. × (25 ft. - 2.5 ft.) + Other boy's weight × (25 ft. - 5 ft.)

Simplifying this equation:

62 lb. × 22.5 ft. + 76 lb. × 20 ft. = 96 lb. × 22.5 ft. + Other boy's weight × 20 ft.

Now, solve for the weight of the other boy:

(62 lb. × 22.5 ft. + 76 lb. × 20 ft. - 96 lb. × 22.5 ft.) / 20 ft. = Other boy's weight

Calculate this expression using a calculator to find the weight of the other boy.