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.
