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the quotient of two numbers is 3 and their sum is 8 what are he two numbers

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Translating Word Equations into Numerical Equations

To change words into equations, we can recognize keywords that translate into operations and/or numbers:

  • quotient = divide
  • a number/the number/two numbers = variables
  • sum = add

Solving the Question

Let the two numbers be a and b.

We're given:

  • quotient of a and b is 3
    ⇒ [tex]\dfrac{a}{b}=3[/tex]
  • sum of a and b is 8
    ⇒ [tex]a+b=8[/tex]

First, isolate a in the first equation and substitute it in the second equation to solve for b:

[tex]\dfrac{a}{b}=3\\\\a=3b[/tex]

[tex]a+b=8\\3b+b=8\\4b=8\\b=2[/tex]

Therefore, one of the numbers is 2. Substitute this into one of our equations to solve for a:

[tex]a+b=8\\a+2=8\\a=6[/tex]

Therefore, the other number is 6.

Answer

The two numbers are 2 and 6.

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