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Dutchess_III's avatar

What is the formula for finding "35% of what number is 84"?

Asked by Dutchess_III (43045points) March 1st, 2011

It’s been a long day, and I can’t get my mind to click. I’m trying to help my daughter who is helping a friend studying for her GED. When they ask questions like the one above, they don’t want the answer, which is easy enough to find. They want the “set up”....the proportion.
My daughter came up with X/.35 = 84/100. Is that correct?

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13 Answers

Soubresaut's avatar

84/x = 35/100 is how I would do it—
The relationship between 84 and x, is that 84 is 35% of x. So, 84 to X is the same proportion as 35 to 100

For hers:
– First, if it’s .35, it should then be 1 instead of 100
– And also, I think what she did was put the figures down in the order they appeared X, 35%, 84? I would work with her on taking apart the words to understand what it’s saying, and then converting those concepts into the numbers?

optimisticpessimist's avatar


DancingMind beat me to it. But here is another way to set up the problem algebraically. It just skips having to work with denominators.

Dutchess_III's avatar

@optimisticpessimist (Hey OP!!) Yes, I came up with .35X=84 to get the answer, but….I’m not sure but she’s thinking they want fractions…...

optimisticpessimist's avatar

@Dutchess III Then DancingMind gave you what you need. 84 is to x what 35 is to 100.

iamthemob's avatar

The above are totally right.

For future reference, when your asked about percentages – know that it will always be in the following format:

x/y = %/100

then you cross multiply and reduce.

x is the constant where you are asked to determine “X is _% of what number” (and therefore y is the variable); and y is the constant where you are asked “What is _% of Y?”

They don’t want fractions here with that question – they want a whole number.

optimisticpessimist's avatar

@DancingMind I’ll get you next time my pretty, hehe.

Dutchess_III's avatar

Fantastic! To me, when you see the “answer” sometimes everything just clicks, effortlessly, you know? I knew all that, but I was trying to be too complicated! @iamthemob Thanks!
OP, got another one for you: If a person weighing 175 jumps out of a 2nd story window, and each story is 12.2335435 feet tall, how long will it take them to hit the ground? You must factor carpeting or no carpeting in.

Mariah's avatar

Everyone has already given you correct answers, but I just wanted to pop in and add something. Rather than memorizing formulas, which are easy to forget, here are some nice rules to fall back on.
“Per cent” is self explanitory: per means division, cent means one hundred. “Of” is math-code for multiplication. “What number” is obviously your unknown, and “is” is your equals sign. I like these rules because it makes it easy to transform an English sentence into an equation. Your sentence above just becomes (35/100)x = 84 and from there it’s just a matter of solving for x.

optimisticpessimist's avatar

@Dutchess_III Okay, that one is a lot more complicated.

Odysseus's avatar

84 / 35 = 2.4

Dutchess_III's avatar

@Mariah Nice!! Who taught you that!

@OP Just think about it! It will awaken you at 3 a.m. with The Answer! :) Welcome home.

@Odysseus Yup. That’s the “answer” but that isn’t what they were looking for…..

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