60 is 20% percent less than what number

Question

I know the answer is 75.

I need the actual equation for solving. As in 60 + .20X = X

That equation seems correct but I'm not able to show my 6th grader how to get the answer.

Answer 1

The correct equation is $X-0.2X=60$ or equivalenly $0.8X=60$, which evaluates to $X=\frac{60}{0.8}=\frac34=75$.

Answer 2

If you want to avoid algebra for some reason (you say you have the equation but can't show your 6th grader how to solve it from there), then here's another way to explain it.

$60$ is $20\%$ less than some number. So $60$ is $80\%\left(=\frac45\right)$ of this number. So this number $\times \frac45$ gives you $60$. So this number must be $60\times\frac54=75$.

Answer 3

Working with number is what has helped me to understand things deeply from 6th grade to now. I can still remember understanding linear algebra with 2 dimension real valued vectors in my head.

Something that would have worked on the 6th grader I was: (italic is the kid answer the rest is what the teacher show / says:

$60$ is $20%$ less than what number x?

Well that number should to be bigger than 60 since it is that number minus something. Let's try $100$: $100 - 20% 100 = 80$ it is too big.

But what do we want? I don't know

What do we want on the right side of the equation? 60

What number on the left side should give us 60? I don't know

60 is 20% less than what number x? What number on the left side should give us 60? x

Replace 100 with x and 80 with 60 in the formula. Oh Ok

I would try to teach equations with something simpler at first maybe. The idea of percentage is tricky and pretty difficult to grasp.

Answer 4

$$ 20 \text {%} \text { less means } 80\text {%} $$

$$ 80 \text {% means 4 out of 5}$$

$$\text {4 out of 5 is 60}$$

$$ \text {What is 5 out of 5 ?}$$

$$ \text {It is 75} $$

Answer 5

What do you know about number X, remembering that $X$ = 100% of $X$?

You know that : 60 is the result of substracting 20% of X from X, or, equivalently,

$100$% of $X$ - $20$% of $X$ = $60$,

which means that :

$80$% of $X = 60$, or

$\frac {80} {100} \times X = 60$.

You finally get $X$ by dividing eaxh side by $\frac {80} {100}$.

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