Let's denote Beckham's mass as \( B \) and his son's mass as \( S \). We are given the following two pieces of information:
1. The total mass of Beckham and his son is 145 kg:
\[ B + S = 145 \]
2. The ratio of Beckham's mass to his son's mass is 23:6, which can be written as:
\[ \frac{B}{S} = \frac{23}{6} \]
From this ratio, we can express Beckham's mass in terms of his son's mass:
\[ B = \frac{23}{6} \cdot S \]
We can now substitute this expression for \( B \) into the first equation:
\[ \frac{23}{6} \cdot S + S = 145 \]
Combine the terms with \( S \):
\[ S \left( \frac{23}{6} + 1 \right) = 145 \]
\[ S \left( \frac{23}{6} + \frac{6}{6} \right) = 145 \]
\[ S \left( \frac{29}{6} \right) = 145 \]
Now solve for \( S \):
\[ S = \frac{145}{\frac{29}{6}} \]
\[ S = 145 \cdot \frac{6}{29} \]
\[ S = 5 \cdot 6 \]
\[ S = 30 \]
Beckham's son weighs 30 kg. Now use the ratio to find Beckham's mass:
\[ B = \frac{23}{6} \cdot 30 \]
\[ B = 23 \cdot 5 \]
\[ B = 115 \]
Beckham weighs 115 kg.
To find the difference in their mass:
\[ B - S = 115 - 30 \]
\[ B - S = 85 \]
The difference in their mass is 85 kg.
Beckham and his son have a total mass of 145 kg. If the ratio of Beckhams mass to his sons mass is 23:6, find the difference in their mass.
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