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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
 one year ago
 one year 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
 one year ago
 one year ago

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

erica123Best ResponseYou've already chosen the best response.0
can you help solve it?
 one year ago

slaaibakBest ResponseYou've already chosen the best response.1
Substitute the x=4y8 into the second equation
 one year ago

slaaibakBest ResponseYou've already chosen the best response.1
you will get (4y 8)y = 60 solve for y. then solve for x
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Here'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.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
i got y=15 and x=68?
 one year ago

erica123Best ResponseYou've already chosen the best response.0
im not positive that thats correct
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
no =( I don't think so.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
i dont know what i did wrong :/
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Show me your work, okay?
 one year ago

erica123Best ResponseYou've already chosen the best response.0
ok 60=(4y8)y 60=4y8y 60/4 = 4y/4 y=15
 one year ago

slaaibakBest ResponseYou've already chosen the best response.1
The problem lies in line 2
 one year ago

erica123Best ResponseYou've already chosen the best response.0
x= 4(15)8 x= 608 x=68
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
distribute, sweet thang.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
whoops! forgot the to square it. but then there are no like terms to combine how would we solve 60= 4y^28y
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Well, 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?
 one year ago

erica123Best ResponseYou've already chosen the best response.0
yes we have to move the 60 over so it becomes a zero so then we have the values a b c for quadratic equation
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Good =) 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.
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Yes =) Take out a common factor of 4 first though.
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
It makes it a lot easier.
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Nooo show me your factoring, please.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
4? isnt is 2 and 2 or 4 and 1?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
noope. show me your factoring.
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
from 4y^2 8y60 = 0
 one year ago

SmoothMathBest 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.
 one year ago

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

erica123Best ResponseYou've already chosen the best response.0
ok after i do the quadratic equation i will get 2 different answers and those will be the answer to the problem right?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Reread the problem and tell me if we have answered the question yet.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
i did but i don't know won't that only find x and not y?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Right. Well actually, it finds y. Right?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
We 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.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
yes it seems so confusing i got fractions for both answers 1/12 and 1/20 is that correct?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
=/ I don't know what mistake you made.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
i dont know either :(
 one year ago

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

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

erica123Best ResponseYou've already chosen the best response.0
oh i see what i did im sorry i was doing 2ac instead of 2a
 one year ago

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

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

erica123Best ResponseYou've already chosen the best response.0
which variable do i plug into and do i use the 5 or 3?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Okay, 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.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
sorry and yes we know 2 answer to y so then which one would you substitute for x?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Now, 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.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
ok i chose 5 and plugged it into x=4y8 and i got 12
 one year ago

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

erica123Best ResponseYou've already chosen the best response.0
the other possible solution is 55?
 one year ago

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

erica123Best ResponseYou've already chosen the best response.0
wait ! lol sorry im using the wrong equation
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
I have no idea what you're doing. Lol.
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
That's not wrong... but it's not a complete answer.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
but isnt it x= 12, 20
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
The 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.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
but theres 2 x and y values
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Ooooh, goodness. How to explain this...
 one year ago

erica123Best ResponseYou've already chosen the best response.0
lol i dont know what should i do? should i just leave 2 values for both variables?
 one year ago

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

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

SmoothMathBest ResponseYou've already chosen the best response.2
It 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.
 one year ago

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

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

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

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

erica123Best ResponseYou've already chosen the best response.0
yup so i just leave those 2 answers?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Right. And what are those two answers?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
mmmm, I don't like how you wrote that.
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Is x=5 y = 20 a solution?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Try plugging it in if you need to check.
 one year ago

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

SmoothMathBest ResponseYou've already chosen the best response.2
That's what I meant to ask.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
wait no it isnt i just tried it out
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Okay so... is y=5 still good?
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
It's not good when x=20, we decided.
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Alright, why is it still good?
 one year ago

erica123Best ResponseYou've already chosen the best response.0
because when we plug it in 20=4(5)8 it gives us 12 which is not equal to 20
 one year ago

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

erica123Best ResponseYou've already chosen the best response.0
if we plug in 3 it will work
 one year ago

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

erica123Best ResponseYou've already chosen the best response.0
oh sorry lol so i can just leave both numbers?
 one year ago

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

SmoothMathBest ResponseYou've already chosen the best response.2
Great. That's one answer.
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
As a SECOND. SEPARATE answer
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
you could do 5 and 12
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
So, 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
 one year ago

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

erica123Best ResponseYou've already chosen the best response.0
no 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
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Well, 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."
 one year ago

erica123Best ResponseYou've already chosen the best response.0
oh 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
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
Yeah, 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.
 one year ago

SmoothMathBest ResponseYou've already chosen the best response.2
For 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.
 one year ago

erica123Best ResponseYou've already chosen the best response.0
yeah 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
 one year ago

erica123Best ResponseYou've already chosen the best response.0
goodnight and thanks so much once again! you have been an amazing help!
 one year ago
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