Question

A bag contains two steel balls and five brass balls. The total weight of the bag is 13 pounds. If two steel balls are added and two brass balls are removed, the bag’s weight decreases to 12 pounds. If s is the weight of a steel ball and b is the weight of a brass ball, the system of linear equations representing this situation is? Solving the system of linear equations, the weight of a steel ball is ? and the weight of a brass ball is?

Answer 1

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

multiply the top equation by two: 4s+10b=26
You can find 7b=14

Each brass ball is 2 pounds.
Then plug this amount back into the equation to get each steel ball is 1.5 pounds.

Answer 2

The linear equations are 2s + 5b = 13 , 4s + 3b = 12 and the weight of a steel ball is 1.5 pound , the weight of the brass ball is 2 pound .

Explanation:

As

s is the weight of a steel ball and b is the weight of a brass ball.

As given

A bag contains two steel balls and five brass balls.

The total weight of the bag is 13 pounds.

Equation becomes

2s + 5b = 13

As given

If two steel balls are added and two brass balls are removed, the bag’s weight decreases to 12 pounds.

4s + 3b = 12

Thus linear equation becomes

2s + 5b = 13

4s + 3b = 12

Thus multiply 2s + 5b = 13 by 2 and subtracted from 4s + 3b = 12 .

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

-7b = -14

`b = (14)/(7)`

b = 2 pound

Put the value of b in the equation 2s + 5b = 13 .

2s + 5 × 2 = 13

2s + 10 = 13

2s = 13 - 10

2s = 3

`s = (3)/(2)`

s = 1.5 pound

Therefore the linear equations are 2s + 5b = 13 , 4s + 3b = 12 and the weight of a steel ball is 1.5 pound , the weight of the brass ball is 2 pound .