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erica123
 2 years ago
one integer is 8 less than 4 times another integer. the product of the two integers is 60. What are the two integers? show work
erica123
 2 years ago
one integer is 8 less than 4 times another integer. the product of the two integers is 60. What are the two integers? show work

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slaaibak
 2 years ago
Best ResponseYou've already chosen the best response.1Call the one integer x. call the other one y x = 4y  8 xy = 60 Solve this.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0can you help solve it?

slaaibak
 2 years ago
Best ResponseYou've already chosen the best response.1Substitute the x=4y8 into the second equation

slaaibak
 2 years ago
Best ResponseYou've already chosen the best response.1you will get (4y 8)y = 60 solve for y. then solve for x

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Here's the process, my little sugarplum: Pick your favorite equation and your favorite variable in that equation. Solve for that variable. Now, use that to substitute into the OTHER equation. This will give you an equation with just one variable in it =) Solve for that variable, and you should just get a number. Now, you know one variable, so you can look back at either of the first equations and use that variable to solve for the other one.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0i got y=15 and x=68?

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0im not positive that thats correct

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2no =( I don't think so.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0i dont know what i did wrong :/

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Show me your work, okay?

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0ok 60=(4y8)y 60=4y8y 60/4 = 4y/4 y=15

slaaibak
 2 years ago
Best ResponseYou've already chosen the best response.1The problem lies in line 2

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0x= 4(15)8 x= 608 x=68

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2distribute, sweet thang.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0whoops! forgot the to square it. but then there are no like terms to combine how would we solve 60= 4y^28y

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Well, that's a whole 'nother kind of problem, and I'm guessing you've actually had a lot of practice with it, but it can be tricky, I understand. The most common ways are factoring or quadratic formula. Sound familiar?

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0yes we have to move the 60 over so it becomes a zero so then we have the values a b c for quadratic equation

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Good =) And actually, if you want to try factoring, it works nicely for this one. But I'm a fan of the quad formula, since it always works.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Yes =) Take out a common factor of 4 first though.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2It makes it a lot easier.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Nooo show me your factoring, please.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.04? isnt is 2 and 2 or 4 and 1?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2noope. show me your factoring.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2from 4y^2 8y60 = 0

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2... okay you aren't good at factoring. That's okay. A lot of people aren't. Use the quadratic formula.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2I only say that because it's a whole different issue. We can work on it another time =)

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0ok after i do the quadratic equation i will get 2 different answers and those will be the answer to the problem right?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Reread the problem and tell me if we have answered the question yet.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0i did but i don't know won't that only find x and not y?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Right. Well actually, it finds y. Right?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2We wrote our two equations. We substituted into one of them and got an equation with just one variable, y. We're now using the quadratic formula to solve for that variable. It's a little bit confusing because we're getting two possibilities for that variable, but we're still only solving for the one variable. We don't know the second variable yet.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0yes it seems so confusing i got fractions for both answers 1/12 and 1/20 is that correct?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2=/ I don't know what mistake you made.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2\[\frac{b \pm \sqrt{b^2  4ac}}{2a} = \frac{(8) \pm \sqrt{(8)^24(4)(60)}}{2(4)}\]

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2You probably just messed up on a sign somewhere. Did you plug in like that?

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0oh i see what i did im sorry i was doing 2ac instead of 2a

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Good. Except we were solving for y. It's important because of the next step.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2When I go back and plug into the original equation, I want to make sure I plug into the right variable.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0which variable do i plug into and do i use the 5 or 3?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Okay, when you do this kind of problem, it's not important which variable you solve for first. You picked y. That's fine. What's not fine is that halfway through the problem, you started calling it x. Do you understand? You were solving for y, and then you randomly renamed it x. This will cause problems. You solved for y. Don't rename it and there won't be any confusion. So now you know y, so obviously that's what you can substitute in for.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0sorry and yes we know 2 answer to y so then which one would you substitute for x?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Now, I understand that it's a little confusing that you get two answers for y. Try not to be confused by it. It just means that there are two possible answers to the question. One is when y=5 and the other is when y = 3. Whichever one you pick, you'll get an x value that goes along with that y value.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0ok i chose 5 and plugged it into x=4y8 and i got 12

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Good =) So one possible solution is: x=12 y =5 Understand? Find the other possible solution.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0the other possible solution is 55?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Woah there. Where'd 55 come from? You makin' guesses or somethin'?

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0wait ! lol sorry im using the wrong equation

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2I have no idea what you're doing. Lol.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2That's not wrong... but it's not a complete answer.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0but isnt it x= 12, 20

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2The question asks you what the two variables are. The two variables are x and y. It turns out this problem has two possible answers, but a good answer should give me an x value and a y value.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0but theres 2 x and y values

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Ooooh, goodness. How to explain this...

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0lol i dont know what should i do? should i just leave 2 values for both variables?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Alright, stop worrying so much about the correct answer and let's just consider the question, okay?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2The question is talking about a couple of numbers. We called them x and y. And it told us something about those numbers.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2It told us that that their product is 60. We wrote an equation about that. And it told us that one number was 8 less than 4 times the other. We wrote an equation about that.

slaaibak
 2 years ago
Best ResponseYou've already chosen the best response.1Two solution sets. (5,12) and (3, 20) That's all you need to know

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2And we're just trying to figure out two numbers that those things are true for.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2So our answer should be two numbers. We happened to name them x and y, so our answer will look like x= y=

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Well, it turns out, there's more than one possible pair of numbers.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0yup so i just leave those 2 answers?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Right. And what are those two answers?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2mmmm, I don't like how you wrote that.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Is x=5 y = 20 a solution?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Try plugging it in if you need to check.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Sorry, my mistake. Is y = 5 x=20 a solution?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2That's what I meant to ask.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0wait no it isnt i just tried it out

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Okay so... is y=5 still good?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2It's not good when x=20, we decided.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Alright, why is it still good?

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0because when we plug it in 20=4(5)8 it gives us 12 which is not equal to 20

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Okay, that tells me why y=5 x=20 is not a solution. Is y =5 bad in general then? Is x=20 bad?

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0if we plug in 3 it will work

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Ahhhhhh my point isn't that they are bad COMPLETELY. My point is just that they don't work TOGETHER.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0oh sorry lol so i can just leave both numbers?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Your answer really needs to be two numbers that work together. What are two numbers that work together?

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Great. That's one answer.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2As a SECOND. SEPARATE answer

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2you could do 5 and 12

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2So, to clarify, you wrote y = 5, 3 x = 12, 20 Which doesn't make it obvious which number goes with which. If you write it this way, it's much more clear y=5 x=12, and y=3 x=20

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2I know it probably seems unimportant, but writing it the first way really shows that you don't understand the question or your answer.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0no it does seem important, thanks so much once again for your help it really means alot =D but i must go because its getting pretty late here

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Well, if the problem was written as an actual reallife problem, it would be easier to explain why it was important. For example, maybe these numbers we're trying to solve for are x=pack of skittles purchased y = number of snickers bars purchased My answer would say something like "Oh, you EITHER bought 5 packs of skittles and 12 snickers bars OOOOR you bought 3 packs of skittles and 20 snickers bars" (shhh please ignore the fact that you can't buy a negative numer of snicker bars) Your answer would say something like, "You bought 5 packs of skittles and 3 packs of skittles. And the number of snickers bars you bought is 12. And also 20."

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0oh yeahhh! i like how you related it to real life lol and yeah so it really is possible to have negatives in our answer as long as it works together

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2Yeah, we can have negatives =) If we're solving real life problems, a lot of times we'll get negative answers. Those negative answers might make sense, or they might not and we might ignore them.

SmoothMath
 2 years ago
Best ResponseYou've already chosen the best response.2For example, if our problem was about money, then the positive answer might mean we made money and the negative answer might mean we lost money. However, if the problem we're solving is about how many children someone has and we got one negative answer and one positive answer, well we'd take the positive one and ignore the negative one because there is no way to have negative children.

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0yeah i see where you're going at and what you'tr trying to say. im sorry to end this convo but i have to leave to get some sleep because im up early in the morning tomorrow

erica123
 2 years ago
Best ResponseYou've already chosen the best response.0goodnight and thanks so much once again! you have been an amazing help!
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