there are 3 numbers, a,b and c. the sum of a and b is 15.31 , the sum of b and c is 9.54,and the sum of a and c is 5.15. find the sum of a,b and c.
To find the sum of numbers a, b, and c, we need to solve the given system of equations:
Equation 1: a + b = 15.31
Equation 2: b + c = 9.54
Equation 3: a + c = 5.15
There are several methods to solve this system of equations. One common approach is to use substitution.
Step 1: Solve Equation 3 for c in terms of a: c = 5.15 - a
Step 2: Substitute the value of c into Equation 2:
b + (5.15 - a) = 9.54
Step 3: Rearrange Equation 2 to solve for b:
b = 9.54 - 5.15 + a
b = 4.39 + a
Step 4: Substitute the value of b from Equation 2 into Equation 1:
a + (4.39 + a) = 15.31
Step 5: Simplify Equation 1:
2a + 4.39 = 15.31
Step 6: Subtract 4.39 from both sides of Equation 1:
2a = 15.31 - 4.39
2a = 10.92
Step 7: Divide both sides of Equation 1 by 2:
a = 10.92 / 2
a ≈ 5.46
Step 8: Substitute the value of a into Equation 2 to find b:
b = 4.39 + a
b = 4.39 + 5.46
b ≈ 9.85
Step 9: Substitute the values of a and b into Equation 3 to find c:
c = 5.15 - a
c ≈ 5.15 - 5.46
c ≈ -0.31
Step 10: Sum of a, b, and c:
sum = a + b + c
sum ≈ 5.46 + 9.85 - 0.31
sum ≈ 15
Therefore, the sum of a, b, and c is approximately 15.