Rewriting Words as Numbers
To translate a word problem into an equation/equation, we much recognize and change key words into operations or numbers.
- a number/the number/one number = x (and/or y)
- _ more = add that amount
- twice = multiply by 2
Solving the Question
We're given:
- One number is 6 more than another number
- Twice the larger number is 5 times the smaller
Let the first number equal x and let the second equal y.
Translate the sentences into equations:
- One number is 6 more than another number
⇒ [tex]x=y+6[/tex] - Twice the larger number is 5 times the smaller
- ⇒ [tex]2x=5y[/tex]
Use substitution to solve for y:
[tex]2(y+6)=5y\\2y+12=5y\\12=3y\\y=4[/tex]
Answer
The smaller number is 4.
