1. Captain Salamander has 3 pet frogs called Dorris, Borris and Morris. He weighs them to check they are the right weight. However, the frogs will only be weighed two at a time! Dorris and Borris weigh 12lbs altogether. Borris and Morris weigh 16lbs altogether. Dorris and Morris weigh 14lbs altogether. How much does each frog weigh?

Their weights are:

Dorris = 5 lbs

Borris = 7 lbs

Morris = 9 lbs

Step-by-step explanation:

Let the weights of the frogs be:

Dorris = d

Borris = b

Morris = m

given:

d + b = 12 - - - (1)

b + m = 16 - - - (2)

d + m = 14 - - - (3)

from (3)

d + m = 14

m = 14 - d - - - (4)

putting the value of m into equation 2:

b + m = 16

b + (14 - d) = 16

b - d + 14 = 16

b - d = 16 - 14

b - d = 2

b = 2 + d - - - - (5)

putting the value of 'b' in equation 5 into equation (1)

d + b = 12 - - - (1)

where: b = 2 + d - - -  (5)

∴ d + (2 + d ) = 12

d + d + 2 = 12

2d = 12 - 2

2d = 10

∴ d = 10 ÷ 2 = 5

d = 5

putting the value of 'd' into eqn (5)

b = 2 + d - - - - (5)

where d = 5

b = 2 + 5 = 7

b = 7 lbs

to find 'm', let us use eqn (3)

d + m = 14 - - - (3)

where d = 5

∴ 5 + m = 14

m = 14 - 5 = 9

m = 9 lbs

Therefore their weights are:

Dorris = 5 lbs

Borris = 7 lbs

Morris = 9 lbs

The distances are equivalent; the distances from first to second base and second to third base are the same value, the angles formed by first and second base and home plate are the same degree as third and second base and home plate. The two angles are complementary adjacent angles, meaning they share the same side and vertex and equal 90°. This information can be used to infer that we are identifying a square, so the distance from first to home and home to third must be equivalent, as squares have the same length for each side.