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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?

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Answer:

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

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