Anonymous wrote:

Anonymous wrote:If I spent $60 and ended up being 120 percent of my budget, what amount would be 100 percent? How would i calculate this?
I am trying to help my kid with his math homework and I would know how to do it in my head but terrible at explaining. Help!?

You are 20% over at $60. 20% of $60 is 2 x 60, 120, move the decimal one place, .2 is 20%, $12.

Double check your work. If $12 is 20%, then 5x that amount, 5 x 20% = 100%, should be the original amount.

Huh?

Anonymous wrote:Ratios also help some kids with this type of question.
X/100 = 60/120

For some the jump straight to losing the zeros and rearranging doesn't make sense right away.

I still have to start with two fractions and cross multiply so I can make sure I get all the numbers in the right spot.

OP, you know how to do this problem, I’m sure of it! I think of word problems having two parts - the computation part and the problem solving part. The computation part can impede your understanding of the problem solving part. When you come across a word problem that seems tricky, try changing the numbers to simpler numbers so you can focus on the problem solving part.

For example, instead of

If I spent $60 and ended up being 120 percent of my budget, what amount would be 100 percent?

Try

If I spent $60 and ended up being 50% of my budget, what about would be 100%?

You probably know that the answer is $120 without having to use an equation or a variable. Now you know that you understand the problem, but it just seems harder because of the numbers. So you have $60 and 50% - how do you use those numbers to arrive at $120? Yes, you can change 50% to 1/2 and multiply by 2 or divide by 1/2. Or change 50% to 0.5 and multiply by 2 or divide by 0.5, but I think fractions are easier to deal with than decimals. If your problem solving works for simpler numbers, it will work for any numbers. It could be

If I spent ln(cos 60 - pi/3) and it ended up being 17,302,927% of my budget, what would be 100%?

and you would still do the problem the same way.

60/120 = X/100

60 × 100 ÷ 120 = 50

(60 divided by 120) X 100

Anonymous wrote:I did x over 60 equals 100 over 120.

Then 60x100 then divide by 120 equals $50.

Same. Most straightforward way I think.

I am a math teacher and reading this is giving me so many warm fuzzies. Look at the half dozen different ways peoples’ brains work! How cool!

The 1.2 posters have the equation, but to figure out how to set that equation up....

First determine what you are solving for: what is unknown? In this case, that's the budget. Give that the name "x".

Now what do you know about x (aka "the budget")? You know that 120% of it (the budget) is $60.

Hints: "percent of" indicates multiplication. "Is" indicates an equal sign.

So, "120 percent of X is $60" can be written mathematically as:
1.2 times X equals 60
Or
1.2x=60

Anonymous wrote:If I spent $60 and ended up being 120 percent of my budget, what amount would be 100 percent? How would i calculate this?
I am trying to help my kid with his math homework and I would know how to do it in my head but terrible at explaining. Help!?

You can change the words into an equation.

$60 spent is 120% of your budget

“Spent is” means equal or same as
“Of” means multiplied by

$60 = 120% x budget
Budget = $60 \ 120%
Budget = $60 \ 1.2
Budget = $50

https://www.google.com/search?client=ms-android-att-us-revc&sxsrf=AJOqlzUhL16pWlOH_SXJmhjEQxRq-a3BmA:1674091750667&q=double+number+line&tbm=isch&sa=X&ved=2ahUKEwi6j_rgvdL8AhVdlIkEHR6qAScQ0pQJegQIChAB&biw=412&bih=866&dpr=2.63

Double Number Lines are cool. Also called tape diagrams.

Anonymous wrote:I did x over 60 equals 100 over 120.

Then 60x100 then divide by 120 equals $50.

The bold was solving for x.

I did x over 60 equals 100 over 120.

Then 60x100 then divide by 120 equals $50.

Always try to look for 1%. 60 and 120 give you the 1% you need to calculate the amount and/or percentage they are asking.
Those formulas have never helped me because I cannot remember than. Always look for 1% or 100% and make sure the number make sense.
The answer had to be less than 60, right? Because 60 is 120%, but you only need 100%, which is smaller than 120%.
I went to school long time again in SU but all kids learned to calculate percentage.
Try percentage change. Very useful thing to know.

Anonymous wrote:If I spent $60 and ended up being 120 percent of my budget, what amount would be 100 percent? How would i calculate this?
I am trying to help my kid with his math homework and I would know how to do it in my head but terrible at explaining. Help!?

You are 20% over at $60. 20% of $60 is 2 x 60, 120, move the decimal one place, .2 is 20%, $12.

Double check your work. If $12 is 20%, then 5x that amount, 5 x 20% = 100%, should be the original amount.

Anonymous wrote:Giving the algebraic equation is correct, but not helpful for teaching percentage calculations. You need to teach how to determine the equation in the first place.

When I was in sixth grade, we were taught how to set up an “I” chart. When I recently had to teach this topic to 30 new adults just hired for our company, I resurrected the “I” chart.

Let me know if you want more explanation.

Not OP, but I’d be interested in more explanation. I don’t remember “I” charts and didn’t see anything relevant in google.