Can someone tell me how to solve my problem? Do I just start plugging in numbers or is there some rational to figure this out?
Sum of three numbers is -5. First, minus second, plus 4 times the third is -20. The third plus 4 times the first plus the second is -20.
a + b + c = -5
a - b + 4c = -20
4a + b + c = -20
looks like a very simple 3 equation in 3 variables question.
Hint: add the first two, then the last two, and go from there
I got a=-5
b=3
c=-3
The sum of two two numbers is(3). Three times the first number minus the second number equals 27. What are the two numbers
(-6) 24
To solve the problem, we can use a system of equations. Let's assign variables to the three unknown numbers.
Let the first number be A, the second number be B, and the third number be C.
Based on the given information, we can set up three equations:
Equation 1: A + B + C = -5 (The sum of three numbers is -5.)
Equation 2: A - B + 4C = -20 (First minus second, plus 4 times the third is -20.)
Equation 3: 4A + B + C = -20 (The third plus 4 times the first plus the second is -20.)
To solve the system of equations, we can use any method, but let's use the substitution method:
We can solve Equation 1 for A:
A = -5 - B - C
Now substitute A in Equation 2 and Equation 3:
Equation 2: (-5 - B - C) - B + 4C = -20
Equation 3: 4(-5 - B - C) + B + C = -20
Simplify both equations:
Equation 2: -5 - 2B + 3C = -20
Equation 3: -20 - 4B - 4C + B + C = -20
Combine like terms:
Equation 2: -2B + 3C = -15
Equation 3: -3B - 3C = 0
Now, solve Equation 3 for B:
B = -C
Substitute B in Equation 2:
-2(-C) + 3C = -15
Simplify:
2C + 3C = -15
Combine like terms:
5C = -15
Divide both sides by 5:
C = -3
Now that we know C is -3, substitute it back into B = -C:
B = -(-3)
B = 3
Now, we can substitute the values of B (-3) and C (3) into Equation 1:
A + 3 - 3 = -5
A = -5
So the three numbers are A = -5, B = 3, and C = -3.
To check the solution, substitute these values into the original equations and see if they satisfy:
Equation 1: -5 + 3 - 3 = -5 ✔️
Equation 2: -5 - 3 + 4(-3) = -20 ✔️
Equation 3: 4(-5) + 3 - 3 = -20 ✔️
Therefore, the solution to the problem is A = -5, B = 3, and C = -3.