Questions on Word Problems: Problems on percentages, ratios, and fractions answered by real tutors!

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Question 150274: Good Afternoon,
I'm having a problem figuring out the break down of this problem. What percentage is 120 of 84. Can you please break this down step by step to show me how the answer comes up to be 70%?: Good Afternoon,
I'm having a problem figuring out the break down of this problem. What percentage is 120 of 84. Can you please break this down step by step to show me how the answer comes up to be 70%?
Answer by Earlsdon(3748) About Me  (Show Source):
You can put this solution on YOUR website!
Well, the way you have stated the problem..."What percentage highlight(is 120)highlight(of 84)?" the answer would be 142.86% !
But I suspect that you have mis-worded the problem and it should be..."What precentage highlight(of 120) highlight(is 84)?" Here's how you might work this...
Percent means..."out of 100" so when you ask..."What percent?" you can express this as:
x/100 now set this equal to the "is" number (that's 84) over the "of" number (that's 120), so...
x/100 = 84/120 Simplify and solve for x.
x = 84(100)/120
x = 70%.
Question 150274: Good Afternoon,
I'm having a problem figuring out the break down of this problem. What percentage is 120 of 84. Can you please break this down step by step to show me how the answer comes up to be 70%?: Good Afternoon,
I'm having a problem figuring out the break down of this problem. What percentage is 120 of 84. Can you please break this down step by step to show me how the answer comes up to be 70%?
Answer by mangopeeler07(445) About Me  (Show Source):
You can put this solution on YOUR website!
You can simply put 84 over 120 and divide:
84/120=.7000

Now move the decimal over twice to the right to get the percent:
70.00%
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Or you can cross multiply with two fractions:
84/120=x/100

The x is over 100 because you want the percent, not the decimal. This proportion is literally saying, "84 is to 120 as x is to 100". You can also do:

120/84=100/x which is literally saying, "120 is to 84 as 100 is to x". As long as you are consistent, it doesn't matter.

Once you have:
84/120=x/100,

cross multiply.
84(100)=120(x)

Simplify
8400=120x

Divide both sides by 120
70=x

so 70%.
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It doesn't matter which way you do it, so whichever is easier for you to do, by all means, do it that way. I hope I've helped you!