Question

When a number is added to 1/5 of itself, the result is 24. The equation that models this problem is n+ 1/5+n = 24. What is the

Answer 1

Answer:

n = 20

Step-by-step explanation:

If we call "a number" n, the equation modelling that statment is:

$\frac{1}{5}n+n=24$

Now, if we have one whole thing - 5/5 - and add 1/5 of that thing, we'll have a total of 6/5 of it. By that same logic, 1/5 of n + 5/5 of n = 6/5 of n. We can write that fact as

$\frac{6}{5}n=24$

So, we slice this number n up into 5 equal parts, we take 6 of those slices, and that gets us a total value of 24. What would the value of just 1 slice - a single fifth of n - be? Well, we'd just need to divide 24 by 6 to find that

$\frac{1}{5}n=24\div6=4$

And if 1/5 of something is 4, that whole thing, 5/5, must be 5 × 4, or 20! Writing that step out in symbols, we have

$\frac{1}{5} n\times5=4\times5=20=n$

So n = 20.