Help me with this math problem

[Anonymous]

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.

This isn’t correct. You are correct that you are 20% over budget at $60, but you it’s 20% of $50, not 20% of $60.

You got the right answer, but it’s coincidence that the numbers works.

If the problem was

$90 is 150% of budget, what is 100% of the budget? The answer is $60. If we did it your way, you are 50% over at $90. 50% of $90 is $45. So 100% is $90, which isn’t the correct answer.

[Anonymous]

Anonymous wrote:

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.

This isn’t correct. You are correct that you are 20% over budget at $60, but you it’s 20% of $50, not 20% of $60.

You got the right answer, but it’s coincidence that the numbers works.

If the problem was

$90 is 150% of budget, what is 100% of the budget? The answer is $60. If we did it your way, you are 50% over at $90. 50% of $90 is $45. So 100% is $90, which isn’t the correct answer.

I’m pp. Maybe the math teacher can weigh in, but when I read the responses, I get a few warm fuzzies but I mostly think that some posters don’t really understand division. There are posts about cross multiplying and ratios and % over budget, but the essence of this problem is understanding that it is a division problem.

Division is not just dividing cakes into equal parts. There are different ways of thinking about division. I think if you ask the average American to give a real life example of 5 divided by 3, they could do it. For example, how much cake would each person get if you divided 5 cakes among 3 people.
But if you ask them for a real life example of 9/5 divided by 1/2, many wouldn’t be able to do it. I was taught that division can be thought of in 3 ways.

1. Measurement
9/5 divided by 1/2 = how many 1/2 ft sections are in a 9/5 long road?
2. Part of a whole
9/5 divided by 1/2 = if half a road is 9/5, how long is the whole?
3. Product and factors
9/5 divided by 1/2 = if 9/5 is the product, and 1/2 is one factor, what is the other factor?

For the problem “If $60 is 120% of budget, what is the budget?”

I use the 2nd (part of a whole) way of thinking about division. If 120% is $60, what is the whole? I know I have to use division to find the answer.

Division is probably the hardest concept to learn of the basic operations. I notice that the schools teach the measurement model, but not the other two, which makes word problems like OP’s harder to see as a division problem.

[Anonymous]

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 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

This is how I always think about these problems. Rephrase the question to say ‘something is something of another something’, then translate the words into math.