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

Step-by-step 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 $\frac{a}{4} +12$. 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 $\frac{a}{3} -5$. Since they are the same, we have the equation below.

$\frac{a}{4} +12 = \frac{a}{3} -5$

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

$\frac{a}{4} +12 = \frac{a}{3} -5 \\ \frac{a +48}{4} = \frac{a -15}{3} \\ (3)(a +48) = (a - 15)(4) \\ 3a +144 = 4a -60 \\ (60 -3a) + 3a +144 = 4a -60 +(60 -3a) \\ a = 204$

Answer:

Our number must be $204$. I think