Final answer:
To solve this problem, we can set up a system of equations using the given information and solve for the weight of one gold bar and one silver bar. The weight of one gold bar is 22.03 kgs, and the weight of one silver bar is -10.02 kgs.
Step-by-step explanation:
To solve this problem, we can set up a system of equations using the information given. Let's assign variables to the unknowns:
Let x = weight of 1 gold bar (in kgs)
Let y = weight of 1 silver bar (in kgs)
From the first sentence, we know that:
15x + 11y = 220.21
From the second sentence, we know that:
9x + 22y = 180.02
We can now solve this system of equations to find the values of x and y.
First, we will multiply the first equation by 2 and the second equation by 3 to cancel out the y variable:
30x + 22y = 440.42
27x + 66y = 540.06
Next, we will subtract the second equation from the first equation:
3x - 44y = -99.64
Now, we can solve this equation for x:
3x = -44y - 99.64
Dividing both sides by 3, we get:
x = -44/3y - 99.64/3
Now, we can substitute this value of x back into one of the original equations. Let's substitute it into the first equation:
15(-44/3y - 99.64/3) + 11y = 220.21
Simplifying, we get:
-44y - 996/3 + 11y = 220.21
Combining like terms, we get:
-33y - 996/3 = 220.21
Dividing both sides by -33, we get:
y = (220.21 + 996/3)/-33
Calculating, we find:
y = -10.02
Now that we have the weight of 1 silver bar, we can substitute this value back into one of the original equations to solve for x. Let's substitute it into the first equation:
15x + 11(-10.02) = 220.21
Simplifying, we get:
15x - 110.22 = 220.21
Adding 110.22 to both sides, we get:
15x = 330.43
Dividing both sides by 15, we get:
x = 330.43/15
Calculating, we find:
x = 22.03
So, 1 gold bar weighs 22.03 kgs and 1 silver bar weighs -10.02 kgs.