Question

A bag contains 2 steel balls and 5 brass balls. The total weight is 13 pounds. If 2 steel balls are added and 2 brass balls are removed, the weight decreases to 12 pounds. How much does each kind of ball weigh?

Answer 1

steel, 4 pounds; brass, 1 pound
steel, 1.5 pounds; brass, 2 pounds
steel, 0.75 pounds; brass, 3 pounds
steel, 3 pounds; brass, 4 pounds

Answer 2

You can set up a system of equations to solve it.

Answer 3

Ok..

Answer 4

You need to let the variables represent the weights of the balls since that is what we are trying to find.
Let s = weight of a steel ball
Let b = weight of a brass ball

Answer 5

Ok so would it be something like s+b=13

Answer 6

At first, we are told about 2 steel balls and 5 brass balls.
2 steel balls weigh 2s
5 brass balls weigh 5b
Their total weight is 13
That means we can write this equation:
2s + 5b = 13

Answer 7

You're on the right track, but remember it's 2 steel balls and 5 brass balls. That is why it's 2s + 5b on the left side.

Answer 8

Ok

Answer 9

I believe your answer would be Steel : 1.5 pounds and Brass: 2 pounds
Like mathstudent55 said you can use a system of equations. Let S= Steel balls and B= Brass balls
2S+5B=13
4S+3B=12 (This is the second one 2 Steel balls are added and 2 brass balls are removed)
You want to isolate a variable and in this case you can do so if you multiply the first equation by 2 so that you can do 4S - 4S leaving you with one variable.
2(2S+5B)= 13(2)
4S+10B=26
Now you can do 4S+10B=26 - 4S+3B=12
7B=14
B=2 This means that the brass balls weigh 2 pounds.
Now if the brass balls weigh 2 pounds then plug it back into the original equation (either one)
2S+5(2)=13
2S+10=13
2S=3
S=1.5 That is your weight for a Steel ball so your answer is the second choice.

Answer 10

The second time, there are 2 steel balls extra and 2 brass balls fewer, so we get
4s + 3b
We are told the weight is now 12 lb, so we get the equation:
4s + 3b = 12

Answer 11

@WordGEEK Thats exactly what i just got.

Answer 12

That means we have this system of equations:

2s + 5b = 13
4s + 3b = 12

Answer 13

Now we need to solve the system of equations.
There are several methods for doing this, but in this case, addition seems to be easy to do.

Answer 14

Multiply the entire first equation by -2 on both sides.
Then write down the original second equation below it.

-4s - 10b = -26
4s + 3b = 12

Now add the equations. The s terms will add to zero leaving only b.

0 - 7b = -14
-7b = -14

Divide both sides by -2:

b = 2

A brass ball weighs 2 lb

Answer 15

Now you can use either of the two original equations to find s, using the value of b we already know, 2.

2s + 5b = 13
2s + 5(2) = 13
2s + 10 = 13
2s = 3
s = 1.5

A steel ball weighs 1.5 lb

The answer is: a steel ball weighs 1.5 lb, and a brass ball weighs 2 lb

Answer 16

Thanks @mathstudent55 and @WordGEEK

Answer 17

You're welcome.