Question

Question #7a122

Answer 1

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`