Question

Find the number which when divided by 4 and increased by 12 is the same as when it is divided by 3 and decreased by 5

Answer 1

Explanation:

Let's make the number we're finding to be
`a`. So, it says that it will be divided by 4 and then added by 12 if we want this in algebraic expression it will be
`(a)/(4) +12\\`. It's also telling us that that expression is the same thing as our number divided by 3 and subtracted by 5. If we want an expression out of it it well be
`(a)/(3) -5\\`. Since they are the same, we have the equation below.

`(a)/(4) +12 = (a)/(3) -5\\`

All we have to do now is to find
`a`.

`(a)/(4) +12 = (a)/(3) -5 \\ (a +48)/(4) = (a -15)/(3) \\ (3)(a +48) = (a - 15)(4) \\ 3a +144 = 4a -60 \\ (60 -3a) + 3a +144 = 4a -60 +(60 -3a) \\ a = 204`

Answer:

Our number must be
`204`. I think