Question

How do you translate the following into a equation and solve: "The sum of two numbers is eighteen. Two less than three times the smaller is equal to the larger."?

Answer 1

The smaller number `x=5`, and the larger number `y=13`

Explanation:

"The sum of two numbers is eighteen. Two less than three times the smaller is equal to the larger."

Let `x` be the smaller number, and let `y` be the larger number.

`x+y=18`

`-2+3x=y`
`implies color(blue)(y=3x-2)`

Use substitution to find the values of the two numbers.
`x+color(blue)((3x-2))=18`
`4x-2=18`
`4x=20`
`color(red)(x=5)`

`y=3color(red)((5))-2`
`y=13`