The sum of Eric and Bob's weights is 9 times greater than the difference of their weights. The positive difference of their weights is also 240 pounds less than the sum. If Eric weighs less than Bob, find Bob's weight.
I am not sure at all how to solve this, especially how to make sure that Eric weighs less than Bob in the equation. Please help! Thanks! :-)
To solve this problem, let's start by assigning variables to the weights of Eric and Bob.
Let's say Eric's weight is represented by 'E,' and Bob's weight is represented by 'B.'
The problem states that the sum of Eric and Bob's weights is 9 times greater than the difference of their weights. Mathematically, this can be represented as:
E + B = 9(B - E)
Now, let's simplify this equation:
E + B = 9B - 9E
To solve for E, let's move all terms containing E to one side of the equation and all non-E terms to the other side:
E + 9E = 9B - B
Combining like terms:
10E = 8B
Dividing both sides by 10:
E = (8/10)B
E = (4/5)B
Since we know Eric weighs less than Bob, we can assume that the ratio of Eric's weight to Bob's weight is less than one. Therefore, we can rewrite the equation as:
E = (4/5)B < B
Now, let's move on to the second condition, which states that the positive difference of their weights is also 240 pounds less than the sum. Mathematically:
B - E = (E + B) - 240
Substituting the value of E we found earlier:
B - (4/5)B = ((4/5)B + B) - 240
Simplifying the equation:
B - (4/5)B = (9/5)B - 240
Combining like terms:
(5/5)B - (4/5)B = (9/5)B - 240
B/5 = (9/5)B - 240
Now, let's solve for B. Subtract (9/5)B from both sides and bring the B term to one side:
B/5 - (9/5)B = -240
Multiplying both sides by 5 to eliminate the denominators:
B - 9B = -1200
-8B = -1200
Dividing both sides by -8:
B = -1200 / -8
B = 150
Therefore, Bob's weight is 150 pounds.
Note: The negative sign in front of both the B terms is canceled out when dividing by -8.