Question

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

Answer 1

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
  ⇒ $\dfrac{a}{b}=3$
• sum of a and b is 8
  ⇒ $a+b=8$

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

$\dfrac{a}{b}=3\\\\a=3b$

$a+b=8\\3b+b=8\\4b=8\\b=2$

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

$a+b=8\\a+2=8\\a=6$

Therefore, the other number is 6.

Answer

The two numbers are 2 and 6.