# Question #7a122

Nov 20, 2016

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.

$h + g = 83$
$h + b = 64.5 \text{ } \rightarrow b = 64.5 - h$
$g + b = 59.5 \text{ } \rightarrow b = 59.5 - g$

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

$59.5 - g = 64.5 - h \text{ } \leftarrow$ 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.

$h + g = 83$
$h - g = 5$

$2 h = 88$
$h = 44 k g \text{ } \leftarrow$This is Harry's mass

$g = 44 - 5 = 39 k g \text{ } \leftarrow$ This is George's mass

Bruce's mass$= 64.5 - 44 = 20.5 k g$

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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 $39 k g$ and $39 + 5 = 44 k g$