The mass of Aravin to the mass of Bob is in the ratio 17 : 13. If the difference in their masses is 12 kg, find their combined mass.
a/b = 17/13
a-b = 12 (why not b-a=12?)
(b+12)/b = 17/13
13(b+12) = 17b
13b + 156 = 17b
156 = 4b
b=39
a=51
a/b = 51/39 = 3*17/3*13 = 17/13
90
Well, if we have Aravin and Bob, I guess we could say they're a dynamic duo, like Batman and Robin, but without the spandex. Now, let's get to the math!
If the mass ratio of Aravin to Bob is 17:13, we can assume that Aravin weighs 17x kg and Bob weighs 13x kg. And apparently, the difference in their masses is 12 kg.
So, we have 17x - 13x = 12 kg. Solving this simple equation, we have 4x = 12 kg. Which means x = 3 kg.
Now, we can find the weight of Aravin and Bob. Aravin = 17x = 17 * 3 = 51 kg. Bob = 13x = 13 * 3 = 39 kg.
Finally, we can calculate their combined mass by adding their weights: 51 kg + 39 kg = 90 kg.
So, their combined mass is 90 kg. They have quite the gravitational pull, huh?
Let's denote the mass of Aravin as A and the mass of Bob as B.
According to the given information, the ratio of their masses is 17:13. This can be written as A/B = 17/13.
We are also given that the difference in their masses is 12 kg, so we can write A - B = 12.
From the first equation, we can multiply both sides by B to get A = (17/13)B.
Substituting this value of A into the second equation, we get (17/13)B - B = 12.
To combine the terms, we need to find a common denominator for (17/13)B and B, which is 13. So, we multiply the first term by 13/13: (17/13)B * (13/13) = (221/13)B.
Now, the equation becomes (221/13)B - B = 12.
Combining the terms, we have (221B - 13B) / 13 = 12.
Simplifying the numerator, we get 208B / 13 = 12.
Multiplying both sides by 13, we have 208B = 12 * 13.
Solving for B, we get B = (12 * 13) / 208.
B = 78 / 104.
Simplifying further, B = 3/4.
Now, substituting the value of B back into the equation A = (17/13)B, we find A = (17/13) * (3/4).
Multiplying the fractions, we get A = (51/52).
The combined mass of Aravin and Bob is A + B = (51/52) + (3/4).
To add these fractions with different denominators, we need to find a common denominator, which is 52 * 4 = 208.
Rewriting the fractions with the common denominator, we have A = (51/52) * (4/4) = 204/208, and B = (3/4) * (52/52) = 156/208.
Adding the fractions, we get (204/208) + (156/208) = 360/208.
Simplifying the fraction, we find that the combined mass of Aravin and Bob is 180/104 kg.
To find the combined mass of Aravin and Bob, we first need to determine the individual masses of each person.
Given that the ratio of Aravin's mass to Bob's mass is 17:13, we can set up the following equation:
17x = 13y
Where x represents the common factor of Aravin's mass, and y represents the common factor of Bob's mass.
Next, we are given that the difference in their masses is 12 kg:
x - y = 12
Now, we can solve the system of equations simultaneously to find the values of x and y.
From the first equation: 17x = 13y
Divide both sides by 13: x = (13/17)y
Substituting this value of x into the second equation: (13/17)y - y = 12
Simplifying the equation: (13 - 17)y/17 = 12
Multiply both sides by 17: 13 - 17y = 204
Rearranging the equation: -17y = 191
Dividing both sides by -17: y = -191/-17 = 11
Now that we know the value of y, we can substitute it back into the first equation to find x:
17x = 13y
17x = 13(11)
17x = 143
x = 143/17 = 8.42
Therefore, Aravin's mass is approximately 8.42 kg and Bob's mass is 11 kg.
To find their combined mass, we simply add these two values together:
Combined mass = Aravin's mass + Bob's mass
Combined mass = 8.42 kg + 11 kg
Combined mass = 19.42 kg
Therefore, the combined mass of Aravin and Bob is approximately 19.42 kg.