Question

The sum of Jim's weight and Bob's weight is 180 pounds. If you subtract Jim's weight from Bob's weight, you get half of Bob's weight. How many pounds does Bob weigh?

Answer 1

Bob weighs 120 pounds

Explanation:

Our first equation will be J(Jim) + B(Bob) = 180 pounds. Our second equation will be 2J = B because it says " if you subtract Jim's weight from Bob's weight, you get half of Bob's weight." This is basically saying that Jim is half of Bob's weight. So that's why our second equation is 2J=B. In our first equation, J+b=180, if we substitute b for 2J, our second equation, then we get the equation 3J = 180. After dividing 3 from both sides, we get j=60. Since Bob weighs twice as much as Jim, his weight will be 120. Now if we want to double-check, we can substitute Jim and Bob's weight for all of the equations.

1) 60 + 120 = 180 This equation is correct

2) 2(60) = 120 This is correct because 2 times 60 equals to 120

3) 3(60) = 180 This is correct because 60 times 3 equals to 180

Answer 2

120 pounds

Explanation:

We can use systems of equations to solve this problem. Assuming j is Jim's weight and b is Bob's weight, the equations are:

j + b = 180

b - j = 1/2b

Let's get b - j = 1/2b into standard form (b, then j, then the equal sign, then the constant.)

`b - j = (b)/(2)\\(b)/(2) - j = 0`

Now we can solve using the process of elimination.

`b + j = 180\\\\(b)/(2) - j = 0\\\\b + (b)/(2) = 180\\\\b + b \cdot 2 = 180\cdot 2\\3b = 360\\b = 120`

Now we know how much Bob weighs, for fun, let's find Jim's weight by substituting into the equation.

`120 + j = 180\\j = 180-120\\j = 60`

So Bob weighs 120 pounds and Jim weight 60 pounds.

Hope this helped!