Question

One number is 6 more than another. Twice the larger number is 5 times the smaller .

Which is the smaller number

Answer 1

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
  ⇒
  `x=y+6`
• Twice the larger number is 5 times the smaller
• ⇒
  `2x=5y`

Use substitution to solve for y:

`2(y+6)=5y\\2y+12=5y\\12=3y\\y=4`

Answer

The smaller number is 4.