the sum of eric's and bob's weights is 9 times greater than the difference of their weights. the positive difference of their weights is also 240 lbs less than the sum. if eric weighs less than bob, find bob's weight.
i can't find an equation for this. any help is appreciated!!
mel :)
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Let's assign variables to the weights of Eric and Bob. Let E represent Eric's weight and B represent Bob's weight.
According to the problem statement, the sum of Eric's and Bob's weights is 9 times greater than the difference of their weights. This can be written as:
E + B = 9(B - E)
Simplifying this equation, we get:
E + B = 9B - 9E
Combining similar terms:
10E = 8B
Dividing both sides of the equation by 8:
E = (8/10)B
E = (4/5)B
Now, we are told that the positive difference of their weights is also 240 lbs less than the sum. We can write this as:
B - E = (E + B) - 240
Substituting the value of E from the first equation:
B - (4/5)B = ((4/5)B + B) - 240
Multiplying both sides of the equation by 5:
5B - 4B = 5B + 4B - 1200
B = 1200
Therefore, Bob's weight is 1200 lbs.
To solve this problem, let's break it down step by step:
Let's assume:
Eric's weight = E
Bob's weight = B
According to the problem:
1. "The sum of Eric's and Bob's weights is 9 times greater than the difference of their weights" translates to:
E + B = 9(B - E) (equation 1)
2. "The positive difference of their weights is also 240 lbs less than the sum" translates to:
B - E = E + B - 240 (equation 2)
Now, let's solve the equations:
We can rewrite equation 1 as:
E + B = 9B - 9E
Simplifying the above equation, we get:
10E = 8B
Now, let's substitute equation 2 into the above equation:
10E = 8(B - E)
Expanding, we get:
10E = 8B - 8E
Further simplifying, we get:
18E = 8B
Now, since Eric weighs less than Bob:
E < B
We know that Eric's weight cannot be 0, so let's assume E = 1 and solve for B:
Substituting E = 1 into the equation, we get:
18(1) = 8B
18 = 8B
Dividing both sides by 8:
B = 18/8
B = 2.25
Therefore, if Eric weighs less than Bob, Bob's weight is 2.25 pounds.
Let me know if you need further assistance!
Let E stand for Eric's weight and B stand for Bob's weight.
From the first sentence:
E + B = 9(B - E)
E + B = 9B - 9E
Transposing gives you:
10E = 8B
E = .8B
From the remaining sentences:
B - E = B + E - 240
Substitute .8B for E in the second equation to solve for B. Put that value in the first equation to find E. Check by putting both values in the second equation.
I hope this helps. Thanks for asking.