Math Problem Statement

If a=13968 b+c=7916 d+e=6836 e+f=10872 f+g=15808 g+h=16487 h+i=22924 c+i=19123 a+h=21988 d+g=6610 what is the value of b

Solution

To solve for bb, we will systematically use the given equations and simplify:

  1. Given:
    • a=13968a = 13968
    • b+c=7916b + c = 7916
    • d+e=6836d + e = 6836
    • e+f=10872e + f = 10872
    • f+g=15808f + g = 15808
    • g+h=16487g + h = 16487
    • h+i=22924h + i = 22924
    • c+i=19123c + i = 19123
    • a+h=21988a + h = 21988
    • d+g=6610d + g = 6610

Step 1: Solve for hh

From a+h=21988a + h = 21988: h=21988a=2198813968=8020h = 21988 - a = 21988 - 13968 = 8020


Step 2: Solve for ii

From h+i=22924h + i = 22924: i=22924h=229248020=14904i = 22924 - h = 22924 - 8020 = 14904


Step 3: Solve for cc

From c+i=19123c + i = 19123: c=19123i=1912314904=4219c = 19123 - i = 19123 - 14904 = 4219


Step 4: Solve for bb

From b+c=7916b + c = 7916: b=7916c=79164219=3697b = 7916 - c = 7916 - 4219 = 3697


Final Answer:

b=3697b = 3697

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Related Questions:

  1. How would you calculate dd, ee, ff, and gg in this problem?
  2. What is the sum of all the variables in the given equations?
  3. Can these equations be represented and solved using matrix algebra?
  4. What are the relationships between a,h,a, h, and other variables in the system?
  5. How would you interpret this problem geometrically or in terms of a graph?

Tip:

When solving systems of equations, organize variables and known values clearly

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations

Formulas

Substitution and elimination in systems of equations

Theorems

Additive property of equality

Suitable Grade Level

Grades 9-11