Question #7a122

1 Answer
Nov 20, 2016

Answer:

Harry has a mass of 44 Kg and Bruce has a mass of 39 Kg

Explanation:

There are 3 different masses involved - we need to be able to write 3 different equations to find them.

Define the variables first.
Let #h# be Harry's mass, #g# be George's mass and #b# be Bruce's mass.

#h+g = 83#
#h+b = 64.5" "rarr b = 64.5-h#
#g+b= 59.5" "rarr b = 59.5-g#

Find Bruce's mass in terms of the other masses: Note: b=b

#59.5-g = 64.5-h" "larr# re-arrange the equation
#h-g = 64.5-59.5#
#h-g = 5#

We now know that the boys' masses add up to 83 and differ by 5.
Add the two equations together:

#h+g = 83#
#h-g = 5#

#2h = 88#
#h= 44 kg" "larr#This is Harry's mass

#g = 44-5 = 39kg" "larr# This is George's mass

Bruce's mass#= 64.5 - 44 = 20.5kg#

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An alternative method :
We now know that the boys' masses add up to 83 and differ by 5.
Subtract the difference from the total of the masses and divide by 2.

#83-5= 78#
#78 div 2 = 39#

The two masses are therefore #39kg# and #39+5= 44kg#