pre algebra word problem

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Eva used three consecutive numbers as her combination lock. Twice the greatest of these integers is 11 less than three times at least

Oct 19th, 2017

Howdy there Nicole. Hope I can help you with this problem. It sounds really cool and like a critical thinking. I'll try to explain my thought processes so you can get it too.

Twice the greatest is 3 times the least. We can make these into equations.
Where the greatest number can be x, cause we don't know what it is. And the least number can be y, cause we don't know what it is either. The cool thing, is that since the numbers are consecutive, meaning in order, we know that x is 2 greater than y, which means x=y plus 2. This will come in handy later.

We know 2x is 11 less than 3y. So we know that 2x plus 11 will equal 3y. We need one of these variables by itself.
So we'll get rid of the 3 on the side with the y by dividing it.

Now we have y=(2x+11)/3

We have a problem now. We have two variables. We don't know either. At this point you can guess a bunch of numbers and check, and you can absolutely get an answer. But we also know that x is equal to y plus 2. We can use this to get y equal to an actual number.

y=(2(y+2)+11)/3

y=(2y+4+11)/3

y=(2y+15)/3

y=2y/3+15/3

y=2y/3+5

y-5=2y/3

3(y-5)=2y

3y-15=2y

-15=2y-3y

-15=-y

y=15.  so x=17

This means the combination is 15, 16, and 17. We have to check though to make sure, cause we could've made a mistake back there and have the wrong answer now.

We plug back into our original equation: y=(2x+11)/3

15=(2(17)+11)/3

15=(34+11)/3

15=45/3

This is true. Your combination is 15, 16, and 17.

Math can be difficult I know. I'd be happy to help you understand these concepts better in the future.

I promise it's logical, and numbers work, they always make sense. You just gotta know how to logically connect the pieces. I'd be happy to help you Nicole. Just let me know. :)

Do you need any clarification?
Jun 17th, 2015

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Oct 19th, 2017
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Oct 19th, 2017
Oct 20th, 2017
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