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The sum of two numbers is 5, and the difference between the first number and twice the second number is 29.

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Converting Words into Equations

We can convert word problems into equations by translating key terms into operations:

  • sum = we add
  • difference = we subtract
  • twice = multiply by 2
  • is = equals

Solving the Question

We're given:

  • sum of two numbers is 5
  • difference between the first number and twice the second number is 29

Let the first number be a and the second number be b.

Translate the words into numbers:

  • sum of two numbers is 5
    [tex]a+b=5[/tex]
  • difference between the first number and twice the second number is 29
    [tex]a-2b=29[/tex]

Subtract the second equation from the first to isolate b:

[tex](a+b)-(a-2b)\\=a+b-a+2b\\=b+2b\\=3b[/tex]

[tex]5-29\\=-24[/tex]

[tex]3b=-24\\b=-8[/tex]

Therefore b is -8.

Substitute b back into the first equation to find a:

[tex]a+b=5\\a-8=5\\a=13[/tex]

Therefore, a is 13.

Answer

a = 13

b = -8

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