Question

Two numbers differ by 12. Twice the larger number increased by triple the smaller number, totals 104. What are the two numbers?

Answer 1

2 numbers differ by 12
Let... `x` be the larger number
Let..... `y` be the smaller number
Then of course smaller number subtracted by larger number would give positive difference
`x-y=12`
Add `y` to both sides
`x-cancely+cancely=12+y`
`x=12+y`.....(1)

Now, here it says twice the larger number.... means `2xxx=2x` now that is increased by(added to) triple the smaller number, means `3xxy=3y` now that is equal to `104`

jot it down in one equation
`2x+3y=104`.....(2)
Put value of `x` from equation one into equation two
`2xx(12+y)+3y=104`
Multiply
`2xx12+2xxy+3y=104`
`24+2y+3y=104`
Subtract both sides by 24 and add the `2y` and `3y`
`cancel24-cancel24+5y=104-24`
You get
`5y=80`
Transfer `5`
`y=80/5`
`color(red)(y=16`
Put value of `y` in equation one to get value of `x`
`x=12+y`
`x=12+16`
Solve
`color(red)(x=28`

Hope this helps