Question

The sum of two numbers is 94. The larger number is 8 less than twice the smaller number. What is the larger number?

Answer 1

x - the larger number
y - the smaller number

The larger number is 8 less than twice the smaller number:

`x=2y-8`
So the larger number is 2y-8.

The sum of the two numbers is 94.

`2y-8+y=94 \\ 2y+y=94+8 \\ 3y=102 \\ y=(102)/(3) \\ y=34`
The smaller number is 34.


`x=2y-8=2 * 34-8=68-8=60`
The larger number is 60.

Answer 2

`a+b=94`


`a>b` ⇒
`a=2b-8`


`\hbox{We will introduce this in the first, original equation} : 2b-8+b=94`


`3b=102` ⇒
`b= (102)/(3)` ⇒
`\boxed{b=34}`


`a=94-34` ⇒
`\boxed{a=60}`