We have a system of three linear equations with three unknowns. Red plus Black equals 20, Red plus White equals 16, and White plus Black equals 12. We need to find the values of Red, Black, and White.
Let's define our variables clearly. We'll use R for Red, B for Black, and W for White. This transforms our word problem into a mathematical system of three linear equations: R plus B equals 20, R plus W equals 16, and W plus B equals 12.
Now we'll use a clever strategy. We add all three equations together. R plus B equals 20, plus R plus W equals 16, plus W plus B equals 12. This gives us 2R plus 2B plus 2W equals 48. Dividing by 2, we get R plus B plus W equals 24.
Now we can find each variable by subtracting each original equation from our sum. To find W, we subtract equation 1: 24 minus 20 equals 4, so W equals 4. To find B, we subtract equation 2: 24 minus 16 equals 8, so B equals 8. To find R, we subtract equation 3: 24 minus 12 equals 12, so R equals 12.
Our final answer is Red equals 12, Black equals 8, and White equals 4. Let's verify this solution by substituting back into our original equations. 12 plus 8 equals 20, check. 12 plus 4 equals 16, check. 4 plus 8 equals 12, check. All equations are satisfied, confirming our solution is correct.