Answer:
Explanation:
You can solve for a, b, and c by using a system of linear equations.
Starting with the first equation:
a + b + c = 90
You can isolate a by subtracting b and c:
a = 90 - b - c
Next, substitute the expression for a into the second equation:
12(90 - b - c) + 10b + 6c = 870
Expanding the equation:
1080 - 12b - 12c + 10b + 6c = 870
Combining like terms:
1070 - 2b + -6c = 870
Adding 2b and 6c to both sides:
1070 = 870 + 2b + 6c
Subtracting 870 from both sides:
200 = 2b + 6c
Dividing both sides by 2:
100 = b + 3c
Finally, subtracting 3c from both sides:
100 - 3c = b
To find c, substitute the expressions for a and b back into the first equation:
a + b + c = 90
90 - b - c + b + c = 90
90 - c = 90
-c = 0
Therefore, c = 0.
To find b, substitute c = 0 into the expression for b:
100 - 3c = b
100 = b
Therefore, b = 100.
Finally, to find a, substitute b = 100 and c = 0 into the expression for a:
a = 90 - b - c
a = 90 - 100 - 0
a = -10
Note that negative values for a, b, and c are possible, but not necessarily meaningful for this specific problem or context.
The solution is:
a = -10
b = 100
c = 0