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# How do you solve this word problem? Topic: What a word for problem solving
July 17, 2019 / By Noland
Question: The problem is "Five divided by the difference of a number and 12 equals the quotient of 10 and the sum of the number and 5. Find the number." Please solve it for me and explain how you solved, because I am confused. ## Best Answers: How do you solve this word problem? Kurt | 8 days ago
You need to first parse the phrases and then create an equation. We always go to the deepest level and then parse back up, just like parenthesis in expressions. You can also think of phrases as having parenthesis around them. "Five divided by the difference of a number and 12" There are two phrases separated by divided by. 5 and "the difference of a number and 12" "the difference of a number and 12" what does this mean. If you have trouble with "of a number", change "of a number" to some number like 7. What does "the difference of 7 and 12" mean. Does it mean 7-12 or 12-7. You could argue that the difference between two things would always be a positive number, but in mathematics we translate this into x - 12. If it had been "the difference of 12 and a number" we would have gotten 12 - x. So after some time we conclude "Five divided by the difference of a number and 12" means 5/(x - 12). Now we have the other phrase separated by "equals" of "the quotient of 10 and the sum of a number and 5". This has two phrases that starts with "the quotient of" which means in math terms division again. The two phrases are 10 and "the sum of a number and 5". We now have another pair of phrases which starts with "the sum of", which means addition. followed by "a number" and 5. This means x + 5. Going back to the "the quotient of" 10 and x+5 means 10/(x+5). Now we have two expression separated by "equals" so we get the equation 5/(x+12) = 10/(x+5) Which can be solved by cross multiplying 5(x+5) = 10(x+12) 5x + 25 = 10x + 120 25 = 5x + 120 5x = -95 x = -19 If you have issues with word problems, I found Sparks Outlines has a book on math word problems that does a very good job of explaining all of this.
👍 204 | 👎 8
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We found more questions related to the topic: What a word for problem solving Originally Answered: How do you solve this word problem?
You need to first parse the phrases and then create an equation. We always go to the deepest level and then parse back up, just like parenthesis in expressions. You can also think of phrases as having parenthesis around them. "Five divided by the difference of a number and 12" There are two phrases separated by divided by. 5 and "the difference of a number and 12" "the difference of a number and 12" what does this mean. If you have trouble with "of a number", change "of a number" to some number like 7. What does "the difference of 7 and 12" mean. Does it mean 7-12 or 12-7. You could argue that the difference between two things would always be a positive number, but in mathematics we translate this into x - 12. If it had been "the difference of 12 and a number" we would have gotten 12 - x. So after some time we conclude "Five divided by the difference of a number and 12" means 5/(x - 12). Now we have the other phrase separated by "equals" of "the quotient of 10 and the sum of a number and 5". This has two phrases that starts with "the quotient of" which means in math terms division again. The two phrases are 10 and "the sum of a number and 5". We now have another pair of phrases which starts with "the sum of", which means addition. followed by "a number" and 5. This means x + 5. Going back to the "the quotient of" 10 and x+5 means 10/(x+5). Now we have two expression separated by "equals" so we get the equation 5/(x+12) = 10/(x+5) Which can be solved by cross multiplying 5(x+5) = 10(x+12) 5x + 25 = 10x + 120 25 = 5x + 120 5x = -95 x = -19 If you have issues with word problems, I found Sparks Outlines has a book on math word problems that does a very good job of explaining all of this. Irving
This would be 5/(x-12)=10/(x+5). Now you could cross-multiply which gets rid of the fractions. 5(x+5) =10(x-12). Now distribute.5x +25 =10x-120. Now subtract 5x and add 120 and get 145=5x; divide by 5 and get 29=x. When you put that back in the original fractions if you want to check it, you get 5/17=10/34, which is true.
👍 80 | 👎 2 Farley
Yes you can label the variable x as width and length can be x + 12 make an equation 2x + 2(x+12) = 156 because you add all sides to get perimeter then u solve for x yielding the answer x = 33 = width x + 12 = 45 = length
👍 73 | 👎 -4 Crispin
let x be the number equation: 5/(x-12) = 10/(x+5) solution: multiply both sides by (x+5) and (x-12) to eliminate denominators (x-12)(x+5) [5/(x-12) = 10/(x+5)] (x-12)(x+5) distribute 5(x+5) = 10(x-12) 5x + 25 = 10x -120 5x - 10x = -120 - 25 -5x = -145 x = 29
👍 66 | 👎 -10 Originally Answered: What's the way to solve this problem with my husband?
So basically, you have a baby and work as a full time mom, you dont "get off of work", your job is 24 hours a day 7 days a week and he thinks he can just waltz in the door and forget reality and that life still has to happen at home? Next time he yells at you, say this, "When is MY time off? When do I get a break?" Then walk away. Look hon, all men are like that until they realize how hard it truly is. You know how I got my husband to realize it? I left him alone with the kids for a day while I went shopping and went to a bookstore and had peace and quiet while I read a book. When I got home, he apologized and I never heard a word from him again when I ask him to do something. It takes two for a relationship to work, and yes, he might have a difficult job, but so do you! Raising children aren't easy and he needs to realize that or you will grow to resent him.

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