The average mass of Ken, David and Kelvin is 42 kg. David is 6 kg heavier than the average mass of Ken and Kelvin. Ken is 6kg heavier than Kelvin. Find David's mass.
Kelvin --- x
Ken ----- x+6
average of Kelvin and Ken = (2x+6)/2 = x+3
David = (x+3) + 6 = x+9
(x + x+6 + x+9)/3 = 42
3x + 15 = 126
3x = 111
x = 111/3 = 37
David is 37+9 = =46
check:
Kelvin --> 37
Ken----> 43
David ---> 46
average of Kelvin and Ken = (37+43)/2 = 40
Is David 6 more than that ? YES
All is good
Let's assign variables to the masses of Ken (K), David (D), and Kelvin (Kv).
Given:
The average mass of Ken, David, and Kelvin = 42 kg
David is 6 kg heavier than the average mass of Ken and Kelvin.
Ken is 6 kg heavier than Kelvin.
Let's set up the equations based on the given information.
1. Average mass = (Ken + David + Kelvin) / 3
42 = (K + D + Kv) / 3 -- Equation 1
2. David's mass = Average mass + 6 kg
D = (K + D + Kv) / 3 + 6 -- Equation 2
3. Ken's mass = Kelvin's mass + 6 kg
K = Kv + 6 -- Equation 3
Now, we will solve these equations to find David's mass.
Let's substitute Equation 3 into Equation 2:
D = (Kv + 6 + D + Kv) / 3 + 6
D = (2Kv + D + 12) / 3 + 6
Multiply both sides of the equation by 3 to eliminate the fraction:
3D = 2Kv + D + 12 + 18
2D - D = 2Kv + 30
D = 2Kv + 30 -- Equation 4
Substitute Equation 3 into Equation 1:
42 = (K + D + Kv) / 3
42 = (Kv + 6 + 2Kv + 30 + Kv) / 3
Multiply both sides of the equation by 3 to eliminate the fraction:
3*42 = 4Kv + 36 + 90 + 3Kv
126 = 7Kv + 126
7Kv = 126 - 126
7Kv = 0
Kv = 0 / 7
Kv = 0 kg
Substitute Kv = 0 into Equation 4 to find D:
D = 2(0) + 30
D = 0 + 30
D = 30 kg
Therefore, David's mass is 30 kg.
To solve this problem, let's assign variables to the unknown quantities. Let K represent the mass of Ken, D represent the mass of David, and X represent the mass of Kelvin.
We are given two pieces of information:
1) The average mass of Ken, David, and Kelvin is 42 kg:
(K + D + X)/3 = 42
2) David is 6 kg heavier than the average mass of Ken and Kelvin:
D = (K + X)/2 + 6
We can use these two equations to solve for the values of K, D, and X. Let's start by rearranging the first equation:
K + D + X = 42 * 3
K + D + X = 126
Now, substitute the value of D from the second equation into the rearranged first equation:
K + (K + X)/2 + 6 + X = 126
Next, simplify this equation:
K + K/2 + X/2 + 6 + X = 126
(2K + K + X + 2X)/2 + 6 = 126
(3K + 3X)/2 + 6 = 126
Now, multiply both sides of the equation by 2 to eliminate the fraction:
3K + 3X + 12 = 252
Simplify further:
3K + 3X = 252 - 12
3K + 3X = 240
Finally, divide both sides of the equation by 3 to isolate K and X:
K + X = 240/3
K + X = 80
Now, let's use the given information that Ken is 6 kg heavier than Kelvin:
K = X + 6
Substitute this into the K + X = 80 equation:
X + 6 + X = 80
2X + 6 = 80
2X = 80 - 6
2X = 74
X = 37
Now we know that Kelvin's mass is 37 kg.
Substitute this value back into the K = X + 6 equation to find Ken's mass:
K = 37 + 6
K = 43
Now we have both Ken's (K = 43 kg) and Kelvin's (X = 37 kg) masses.
Lastly, substitute these values into the second equation to find David's mass:
D = (43 + 37)/2 + 6
D = 80/2 + 6
D = 40 + 6
D = 46
Therefore, David's mass is 46 kg.